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Trudy Mat. Inst. Steklova, 2001, Volume 232, Pages 115–143 (Mi tm208)  

This article is cited in 32 scientific papers (total in 32 papers)

Sharp Estimates for the Norms of Hardy-Type Operators on the Cones of Quasimonotone Functions

M. L. Gol'dman


Abstract: Order-sharp three-weight estimates are established for the norms of restrictions of generalized Hardy operators onto the cones of functions from Lebesgue spaces that are monotone on a positive half-axis. The necessary and sufficient conditions are obtained for the boundedness of the norms under minimal a priori assumptions about the measures involved in the definitions of Hardy operators and weighted Lebesgue spaces. The uniformity of the estimates with respect to the parameters of the problem is observed.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 232, 109–137

Bibliographic databases:
UDC: 517
Received in October 2000

Citation: M. L. Gol'dman, “Sharp Estimates for the Norms of Hardy-Type Operators on the Cones of Quasimonotone Functions”, Function spaces, harmonic analysis, and differential equations, Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 232, Nauka, MAIK Nauka/Inteperiodika, M., 2001, 115–143; Proc. Steklov Inst. Math., 232 (2001), 109–137

Citation in format AMSBIB
\Bibitem{Gol01}
\by M.~L.~Gol'dman
\paper Sharp Estimates for the Norms of Hardy-Type Operators on the Cones of Quasimonotone Functions
\inbook Function spaces, harmonic analysis, and differential equations
\bookinfo Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2001
\vol 232
\pages 115--143
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm208}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1851444}
\zmath{https://zbmath.org/?q=an:1030.42013}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 232
\pages 109--137


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. L. Gol'dman, R. A. Kerman, “On Optimal Embedding of Calderon Spaces and Generalized Besov Spaces”, Proc. Steklov Inst. Math., 243 (2003), 154–184  mathnet  mathscinet  zmath
    2. Goldman M.L., Kerman R., “On the rearrangement invariant hull of a Calderon space”, Dokl. Math., 68:2 (2003), 177–181  mathnet  mathscinet  zmath  isi
    3. Goldman M.L., Sorokina M.V., “Three-weighted Hardy-type inequalities on the cone of quasimonotone functions”, Dokl. Math., 71:2 (2005), 209–213  mathnet  mathscinet  zmath  isi  elib
    4. Cerda J., Coll H., “Function cones and interpolation”, Math. Nachr., 278:3 (2005), 227–239  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Gogatishvili A., Pick L., “A reduction theorem for supremum operators”, J. Comput. Appl. Math., 208:1 (2007), 270–279  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    6. Gogatishvili A., Johansson M., Okpoti C.A., Persson L.-E., “Characterisation of embeddings in Lorentz spaces”, Bull. Austral. Math. Soc., 76:1 (2007), 69–92  crossref  mathscinet  zmath  isi  elib
    7. Gol'dman M.L., “Integral properties of generalized Bessel potentials”, Dokl. Math., 75:3 (2007), 361–366  crossref  mathscinet  zmath  isi  scopus
    8. Cianchi A., “Symmetrization in anisotropic elliptic problems”, Comm. Partial Differential Equations, 32:5 (2007), 693–717  crossref  mathscinet  zmath  isi  elib  scopus
    9. Johansson M., Stepanov V.D., Ushakova E.P., “Hardy inequality with three measures on monotone functions”, Math. Inequal. Appl., 11:3 (2008), 393–413  mathscinet  zmath  isi  elib
    10. Carro M., Gogatishvili A., Martin J., Pick L., “Weighted inequalities involving two hardy operators with applications to embeddings of function spaces”, J. Operator Theory, 59:2 (2008), 309–332  mathscinet  zmath  isi  elib
    11. Cianchi A., Maz'ya V.G., “Neumann problems and isocapacitary inequalities”, J. Math. Pures Appl. (9), 89:1 (2008), 71–105  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Stepanov V.D., Persson L.E., Popova O.V., “Two-sided hardy-type inequalities for monotone functions”, Dokl. Math., 80:3 (2009), 814–817  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    13. Goldman M.L., “Optimal embedding of Bessel- and Riesz-type potentials”, Dokl. Math., 80:2 (2009), 689–693  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    14. Persson L.-E., Popova O.V., Stepanov V.D., “Two-sided Hardy-type inequalities for monotone functions”, Complex Variables and Elliptic Equations, 55:8–10 (2010), 973–989  crossref  mathscinet  zmath  isi  scopus  scopus
    15. Alvino A., Cianchi A., Maz'ya V.G., Mercaldo A., “Well-posed elliptic Neumann problems involving irregular data and domains”, Ann Inst H Poincaré Anal Non Linéaire, 27:4 (2010), 1017–1054  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    16. M. L. Goldman, “Order-sharp estimates for Hardy-type operators on cones of quasimonotone functions”, Eurasian Math. J., 2:3 (2011), 143–146  mathnet  mathscinet  zmath
    17. Goldman M.L., “On equivalent criteria for the boundedness of Hardy type operators on the cone of decreasing functions”, Anal Math, 37:2 (2011), 83–102  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    18. Stepanov V.D., Tikhonov S.Yu., “Two-weight inequalities for the Hilbert transform of monotone functions”, Doklady Mathematics, 83:2 (2011), 241–242  crossref  mathscinet  zmath  isi  elib  elib  scopus
    19. O. V. Popova, “Hardy-type inequalities on the cones of monotone functions”, Siberian Math. J., 53:1 (2012), 152–167  mathnet  crossref  mathscinet  isi
    20. M. L. Goldman, “Order-sharp estimates for Hardy-type operators on the cones of functions with properties of monotonicity”, Eurasian Math. J., 3:2 (2012), 53–84  mathnet  mathscinet  zmath
    21. Gogatishvili A. Stepanov V.D., “Operators on Cones of Monotone Functions”, Dokl. Math., 86:1 (2012), 562–565  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    22. A. Gogatishvili, V. D. Stepanov, “Reduction theorems for weighted integral inequalities on the cone of monotone functions”, Russian Math. Surveys, 68:4 (2013), 597–664  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    23. D. V. Prokhorov, V. D. Stepanov, “On weighted Hardy inequalities in mixed norms”, Proc. Steklov Inst. Math., 283 (2013), 149–164  mathnet  crossref  crossref  mathscinet  isi  elib
    24. M. L. Goldman, “Some equivalent criteria for the boundedness of Hardy-type operators on the cone of quasimonotone functions”, Eurasian Math. J., 4:4 (2013), 43–63  mathnet
    25. Persson L.-E., Popova O.V., Stepanov V.D., “Weighted Hardy-Type Inequalities on the Cone of Quasi-Concave Functions”, Math. Inequal. Appl., 17:3 (2014), 879–898  crossref  mathscinet  zmath  isi  elib  scopus
    26. Taspaganbetova Zh., “Two-Sided Estimates For Matrix Operators on the Cone of Monotone Sequences”, J. Math. Anal. Appl., 410:1 (2014), 82–93  crossref  mathscinet  zmath  isi  elib  scopus
    27. Vasil'eva A.A., “Estimates For Norms of Two-Weighted Summation Operators on a Tree Under Some Restrictions on Weights”, Math. Nachr., 288:10 (2015), 1179–1202  crossref  mathscinet  zmath  isi  scopus  scopus
    28. D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov Integral Operators”, Proc. Steklov Inst. Math., 300, suppl. 2 (2018), 1–112  mathnet  crossref  crossref  zmath  isi  elib
    29. Gogatishvili A. Mustafayev R.Ch., “Weighted Iterated Hardy-Type Inequalities”, Math. Inequal. Appl., 20:3 (2017), 683–728  crossref  mathscinet  zmath  isi  scopus
    30. Alberico A., di Blasio G., Feo F., “A Priori Estimates For Solutions to Anisotropic Elliptic Problems Via Symmetrization”, Math. Nachr., 290:7 (2017), 986–1003  crossref  mathscinet  zmath  isi  scopus  scopus
    31. Gorbachev D., Liflyand E., Tikhonov S., “Weighted Norm Inequalities For Integral Transforms”, Indiana Univ. Math. J., 67:5 (2018), 1949–2003  crossref  mathscinet  zmath  isi
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