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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 6, Pages 1263–1279 (Mi smj1917)  
This article is cited in 6 scientific papers (total in 6 papers)

Pointwise and integral estimates for the $B$-Riesz potential in terms of $B$-maximal and $B$-fractional maximal functions

V. S. Gulieva, N. N. Garakhanovaa, Yu. Zerenb

a Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences
b Harran University
Full-text PDF (355 kB) Citations (6)
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Abstract: We study the maximal and fractional maximal functions and Riesz potentials that are generated by the generalized shift operator associated with the Laplace–Bessel operator. We obtain some pointwise and integral estimates that give a relation between the $B$-maximal and $B$-fractional maximal functions and $B$-Riesz potentials and extend the available results to the objects of a more general nature. Basing on these results, we prove interpolation theorems for the $B$-fractional maximal functions and $B$-Riesz potentials.
Keywords: generalized shift operator, $B$-maximal function, $B$-fractional maximal function, $B$-Riesz potential, Sobolev theorem.
Received: 27.10.2005
Revised: 22.04.2008
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 6, Pages 1008–1022
DOI: https://doi.org/10.1007/s11202-008-0097-6
Bibliographic databases:
UDC: 517.51
Language: Russian
Citation: V. S. Guliev, N. N. Garakhanova, Yu. Zeren, “Pointwise and integral estimates for the $B$-Riesz potential in terms of $B$-maximal and $B$-fractional maximal functions”, Sibirsk. Mat. Zh., 49:6 (2008), 1263–1279; Siberian Math. J., 49:6 (2008), 1008–1022
Citation in format AMSBIB
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\by V.~S.~Guliev, N.~N.~Garakhanova, Yu.~Zeren
\paper Pointwise and integral estimates for the $B$-Riesz potential in terms of $B$-maximal and $B$-fractional maximal functions
\jour Sibirsk. Mat. Zh.
\yr 2008
\vol 49
\issue 6
\pages 1263--1279
\mathnet{http://mi.mathnet.ru/smj1917}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2499099}
\transl
\jour Siberian Math. J.
\yr 2008
\vol 49
\issue 6
\pages 1008--1022
\crossref{https://doi.org/10.1007/s11202-008-0097-6}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-57749175334}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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