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  • 1.
    Aldaz, J. M.
    et al.
    Univ Autonoma Madrid, ICMAT, E-28049 Madrid, Spain.;Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain..
    Barza, Sorina
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Fujii, M.
    Osaka Kyoiku Univ, Dept Math, Kashiwara, Osaka 5828582, Japan..
    Moslehian, Mohammad Sal
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Advances in Operator Cauchy-Schwarz Inequalities and their Reverses2015In: Annals of Functional Analysis, ISSN 2008-8752, E-ISSN 2008-8752, Vol. 6, no 3, p. 275-295Article in journal (Refereed)
    Abstract [en]

    The Cauchy-Schwarz (C-S) inequality is one of the most famous inequalities in mathematics. In this survey article, we first give a brief history of the inequality. Afterward, we present the C-S inequality for inner product spaces. Focusing on operator inequalities, we then review some significant recent developments of the C-S inequality and its reverses for Hilbert space operators and elements of Hilbert C*-modules. In particular, we pay special attention to an operator Wielandt inequality.

  • 2. Arcozzi, N
    et al.
    Barza, Sorina
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Garcia-Domingo, J.L.
    Soria, J.
    Hardys inequalities for monotone functions on partly ordered measure spaces2006In: Proc. Roy. Soc. Edingburgh Sect. A, 136 (2006), no.5Article in journal (Refereed)
  • 3.
    Barza, Sorina
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    A remarkable description of a constant of Muckenhoupt type in a case of multidimensional integral inequalities1997In: A remarkable description of a constant of Muckenhoupt type in a cse of multidimensional integral inequalities / [ed] Anna Klisinka, Lars-Erik Persson, Luleå: Luleå tekniska universitet, 1997Conference paper (Other academic)
  • 4.
    Barza, Sorina
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Multidimensional integral inequalities with homogeneous weights2005In: Gen. Math. Vol. 13, No. 1 (2005)Article in journal (Refereed)
  • 5.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Buse, Constantin
    Rumänien.
    Pecaric, Josep
    Kroatien.
    New characterizations of asymptotic stability for evolution families on Banach spaces2004In: Electronic Journal of Differential Equations, ISSN 1550-6150, E-ISSN 1072-6691, p. 1-9, article id 38Article in journal (Refereed)
  • 6.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Heinig, Hans P.
    Persson, Lars- Erik
    Duality theorems over the cone of monotone functions and sequences in higher dimensions2002In: J. of Inequal. & and Appl., 2002, Vol.7 (1), 79-108Article in journal (Refereed)
  • 7.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Johansson, Maria
    Persson, Lars-Erik
    A Sawyer duality principle for radialy monotone functions in R^n2005In: JIPAM 6, (2005), electronic, 1-13Article in journal (Refereed)
  • 8.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Kaminska, A.
    Persson, L.-E.
    Soria, J.
    Mixed norm and multidimensional Lorentz spaces2006In: POsitivity, 10 (2006), no. 3Article in journal (Refereed)
  • 9.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Kolyada, Viktor
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Soria, Javier
    Department of Applied Mathematics and Analysis, University of Barcelona, Spain.
    Sharp constants related to the triangle inequality in Lorentz spaces2009In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 361, no 10, p. 5555-5574Article in journal (Refereed)
  • 10.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Kravvaritis, D.
    Popa, N.
    Matriceal Lebesgue spaces and Hölder inequality2005In: JFSA, 3(3)(2005)Article in journal (Refereed)
  • 11.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Lie, Victor
    Popa, Nicolae
    Approximation of infinite marices by matricial Haar polynomials2005In: Ark.Mat.,43(2005), 251-269Article in journal (Refereed)
  • 12.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Lind, Martin
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    A new variational characterization of Sobolev spaces2015In: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 25, no 4, p. 2185-2195Article in journal (Refereed)
    Abstract [en]

    We obtain a new variational characterization of the Sobolev space $W_p^1(\Omega)$ (where $\Omega\subseteq\R^n$ and $p>n$). This is a generalization of a classical result of F. Riesz. We also consider some related results.

  • 13.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Marcoci, A.N.
    Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Romania.
    Persson, L.-E.
    Department of Mathematics, Luleå University of Technology.
    Best constants between equivalent norms in Lorentz sequence spaces2012In: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965Article in journal (Refereed)
  • 14.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Marcoci, Anca N.
    Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Romania.
    Marcoci, Liviu G.
    Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Romania.
    Factorizations of Weighted Hardy Inequalities2018In: Bulletin of the Brazilian Mathematical Society, ISSN 1678-7544, E-ISSN 1678-7714, Vol. 49, no 4, p. 915-932Article in journal (Refereed)
    Abstract [en]

    We present factorizations of weighted Lebesgue, Cesàro and Copson spaces, for weights satisfying the conditions which assure the boundedness of the Hardy’s integral operator between weighted Lebesgue spaces. Our results enhance, among other, the best known forms of weighted Hardy inequalities.

  • 15.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Marcoci, Anca Nicoleta
    Technical University of Civil Engineering Bucharest, Department of Mathematics and Computer Science, Bucharest, Romania.
    Marcoci, Liviu Gabriel
    Technical University of Civil Engineering Bucharest, Department of Mathematics and Computer Science, Bucharest, Romania.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Mathematics.
    Optimal estimates in Lorentz spaces of sequences with an increasing weight2013In: Proceedings of the Romanian Academy. Series A Mathematics, Physics, Technical Sciences, Information Science, ISSN 1454-9069, Vol. 14, no 1, p. 20-27Article in journal (Refereed)
  • 16.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Niculescu, C.P.
    Integral inequalities for concave functions2006In: Publ. Math. Debrecen, 68(2006), no. 1-2Article in journal (Refereed)
  • 17.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Niculescu, N. C.
    Strong and weak weighted norm inequalities for the geometric fractional maximal operator2012In: Bulletin of the Australian Mathematical Society, ISSN 0004-9727, E-ISSN 1755-1633, Vol. 86, no 2, p. 205-215Article in journal (Refereed)
  • 18.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Pecaric, Josep
    Persson, Lars-Erik
    Carlson type inequalities1998In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2, no 2, p. 121-135Article in journal (Refereed)
  • 19.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Persson, Lars-Erik
    Luleå tekniska universitet.
    Some new sharp limit Hardy-type  inequalities via convexity2014In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, no 6Article in journal (Refereed)
    Abstract [en]

    Some new limit cases of Hardy-type inequalities are proved, discussed and compared. In particular, some new refinements of Bennett’s inequalities are proved. Each of these refined inequalities contain two constants, and both constants are in fact sharp. The technique in the proofs is new and based on some convexity arguments of independent interest.

  • 20.
    Barza, Sorina
    et al.
    Luleå Tekniska Universitet.
    Persson, Lars-Erik
    Luleå Tekniska Universitet.
    Weighted multidimensional inequalities for monotone functions1999In: Mathematica Bohemica, ISSN 0862-7959, Vol. 124, no 2-3, p. 329-335Article in journal (Refereed)
  • 21. Barza, Sorina
    et al.
    Persson, Lars-Erik
    Burenkov, Viktor
    Pecaric, Josep
    Sharp multidimensional multiplicative inequalities for weighted Lp spaces with homogeneous weights1998In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, no 1, p. 53-67Article in journal (Refereed)
  • 22.
    Barza, Sorina
    et al.
    Luleå universitet.
    Persson, Lars-Erik
    Luleå tekniska Universitet.
    Pecaric, Josep
    Reversed Hölder type inequalities for monotone functions of several variables1997In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 187, p. 67-80Article in journal (Refereed)
  • 23.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Persson, Lars-Erik
    Department of Mathematics, Luleå University of Technology.
    Popa, Emil C.
    epartment of Mathematics, "Lucian Blaga" University of Sibiu, Romania .
    Some multiplicative inequalities for inner products and of the Carlson type2008In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242XArticle in journal (Refereed)
    Abstract [en]

    We prove a multiplicative inequality for inner products, which enables us to deduce improvements of inequalities of the Carlson type for complex functions and sequences, and also other known inequalities.

  • 24.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Persson,, Lars-Erik
    Rakotondratsimba, Yves
    On weighted multidimensional integral inequalities for mixed monotone functions2000In: Bull. Math. Soc. Sci. Math. Roumanie (N.S), ISSN 1220-3874, Vol. 43, no 91, p. 39-45Article in journal (Refereed)
  • 25.
    Barza, Sorina
    et al.
    Karlstad University, Division for Engineering Sciences, Physics and Mathematics.
    Persson, Lars-Erik
    Department of Mathematics, Luleå University.
    Soria, Javier
    Department of Applied Mathematics and Analysis, University of Barcelona, Spain.
    Multidimensional rearrangement and Lorentz spaces2004In: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 104, no 3, p. 203-224Article in journal (Refereed)
    Abstract [en]

    We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional properties of the associated weighted Lorentz spaces.

  • 26.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Persson, Lars-Erik
    Soria, Javier
    Sharp weighted multidimensional integral inequalities for monotone functions2000In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 210, no 1, p. 43-58Article in journal (Refereed)
  • 27.
    Barza, Sorina
    et al.
    Luleå universitet.
    Persson, Lars-Erik
    Soria, Javier
    Sharp weighted multidimensional integral inequalities of Chebysev type1999In: Journal of Mathematical Analysis, ISSN 2217-3412, E-ISSN 2217-3412, Vol. 236, no 2, p. 243-253Article in journal (Refereed)
  • 28.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Persson, L.-E.
    Equivalence of Modular Inequalities of Hardy type on non-negative respective non-increasing functions2008Conference paper (Refereed)
  • 29.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Persson, L-E.
    Popa, N.
    A matriceal analogue of Fejer's theory2003In: Math NachrArticle in journal (Refereed)
  • 30.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Popa, E. C.
    Weighted multiplicative integral inequalities2006In: Journal of inequal pure, ISSN 1443-5756, Vol. 7, no 5, p. 169-175Article in journal (Refereed)
  • 31. Barza, Sorina
    et al.
    Popa, Emil
    Inequalities related to Carlsson's inequality1998In: Tamkang Journal of Mathematics, Vol. 29, p. 59-64Article in journal (Refereed)
  • 32.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Silvestre, Pilar
    Department of Mathematics and Systems Analysis, Aalto University, Finland.
    Functions of bounded second p-variation2014In: Revista Matemática Complutense, ISSN 1139-1138, E-ISSN 1988-2807, Vol. 27, p. 69-91Article in journal (Refereed)
    Abstract [en]

    The generalized functionals of Merentes type generate a scale of spaces connecting the class of functions of bounded second p -variation with the Sobolev space of functions with p-integrable second derivative. We prove some limiting relations for these functionals as well as sharp estimates in terms of the fractional modulus of order 2−1/p . These results extend the results in Lind (Math Inequal Appl 16:2139, 2013) for functions of bounded variation but are not consequence of the last.

  • 33.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Soria, Javier
    Department of Applied Mathematics and Analysis, University of Barcelona, , Spain .
    Sharp constants between equivalent norms in weighted Lorentz spaces2010In: Journal of the Australian Mathematical Society, ISSN 1446-7887, E-ISSN 1446-8107, Vol. 88, no 1, p. 19-27Article in journal (Refereed)
    Abstract [en]

    For an increasing weight w in Bp (or equivalently in Ap), we find the best constants for the inequalities relating the standard norm in the weighted Lorentz space Λp(w) and the dual norm.

  • 34.
    Barza, Sorina
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Stepanov, V.D.
    Persson, L.-E.
    On weighted multidimensional embeddings for monotone functions2001In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 88, no 2, p. 303-319Article in journal (Refereed)
1 - 34 of 34
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