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Tr. Mat. Inst. Steklova, 2008, Volume 260, Pages 264–288 (Mi tm599)  

This article is cited in 12 scientific papers (total in 12 papers)

On the Geometric Mean Operator with Variable Limits of Integration

V. D. Stepanova, E. P. Ushakovab

a Peoples Friendship University of Russia
b Computer Centre Far-Eastern Branch of RAS

Abstract: A new criterion for the weighted $L_p$$L_q$ boundedness of the Hardy operator with two variable limits of integration is obtained for $0<q<q+1\le p<\infty$. This criterion is applied to the characterization of the weighted $L_p$$L_q$ boundedness of the corresponding geometric mean operator for $0<q<p<\infty$.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 260, 254–278

Bibliographic databases:

UDC: 517.51
Received in July 2007

Citation: V. D. Stepanov, E. P. Ushakova, “On the Geometric Mean Operator with Variable Limits of Integration”, Function theory and nonlinear partial differential equations, Collected papers. Dedicated to Stanislav Ivanovich Pohozaev on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 260, MAIK Nauka/Interperiodica, Moscow, 2008, 264–288; Proc. Steklov Inst. Math., 260 (2008), 254–278

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Stepanov V.D., Ushakova E.P., “On boundedness of a certain class of Hardy-Steklov type operators in Lebesgue spaces”, Banach J. Math. Anal., 4:1 (2010), 28–52  crossref  mathscinet  zmath  isi  elib  scopus
    2. Stepanov V.D., Ushakova E.P., “Kernel operators with variable intervals of integration in Lebesgue spaces and applications”, Math. Inequal. Appl., 13:3 (2010), 449–510  mathscinet  zmath  isi  elib
    3. Ushakova E.P., “On boundedness and compactness of a certain class of kernel operators”, J. Funct. Spaces Appl., 9:1 (2011), 67–107  crossref  zmath  isi  elib  scopus
    4. 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
    5. Farsani S.M., “On the Boundedness and Compactness of a Certain Integral Operator”, Banach J. Math. Anal., 7:2 (2013), 86–102  crossref  mathscinet  zmath  isi  elib  scopus
    6. Eveson S.P. Stepanov V.D. Ushakova E.P., “a Duality Principle in Weighted Sobolev Spaces on the Real Line”, Math. Nachr., 288:8-9 (2015), 877–897  crossref  mathscinet  zmath  isi  elib  scopus
    7. Ushakova E.P., “Boundedness Criteria For the Hardy-Steklov Operator Expressed in Terms of a Fairway Function”, Dokl. Math., 91:2 (2015), 197–198  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    8. M. G. Nasyrova, E. P. Ushakova, “Hardy–Steklov operators and Sobolev-type embedding inequalities”, Proc. Steklov Inst. Math., 293 (2016), 228–254  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    9. 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
    10. Prokhorov D.V. Stepanov V.D. Ushakova E.P., “On weighted Sobolev spaces on the real line”, Dokl. Math., 93:1 (2016), 78–81  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    11. E. P. Ushakova, “Alternative boundedness characteristics for the Hardy–Steklov operator”, Eurasian Math. J., 8:2 (2017), 74–96  mathnet  mathscinet
    12. Kalybay A., Oinarov R., Temirkhanova A., “Integral Operators With Two Variable Integration Limits on the Cone of Monotone Functions”, J. Math. Inequal., 13:1 (2019), 1–16  crossref  mathscinet  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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