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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 319, Pages 120–133
DOI: https://doi.org/10.4213/tm4255 (Mi tm4255) 		 
Piecewise General Monotone Functions and the Hardy–Littlewood Theorem

M. I. Dyachenkoab, S. Yu. Tikhonovcde

a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991 Russia
b Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991 Russia
c Universitat Autònoma de Barcelona, Plaza Cívica, 08193 Bellaterra (Cerdanyola del Vallès), Spain
d Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193 Bellaterra (Barcelona), Spain
e ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain
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DOI: https://doi.org/10.4213/tm4255
Abstract: We obtain necessary and sufficient conditions for an integrable piecewise general monotone function to belong to an $L^p$ space with a weight of Muckenhoupt class $\mathbb A_p$ in terms of the Fourier coefficients. We also find a sufficient condition for the Hardy transform of an arbitrary integrable function to belong to the same space.
Funding agency Grant number
Russian Science Foundation 21-11-00131
Ministry of Education and Science of the Republic of Kazakhstan AP14870758
AP14870361
Centre de Recerca Matemàtica PID2020-114948GB-I00
Generalitat de Catalunya 2017 SGR 358
Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R$\&$D CEX2020-001084-M
The study presented in Theorems 1.5, 1.7 and Corollary 1.6 was supported by the Russian Science Foundation under grant no. 21-11-00131, https://rscf.ru/project/21-11-00131/, and performed by M. I. Dyachenko at Moscow State University. The other part of the work was supported in part by the Ministry of Science and Higher Education of the Republic of Kazakhstan (project nos. AP14870758 and AP14870361), Centre de Recerca Matemàtica (grant no. PID2020-114948GB-I00), Generalitat de Catalunya (grant no. 2017 SGR 358), and the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (project no. CEX2020-001084-M).
Received: January 17, 2022
Revised: March 14, 2022
Accepted: April 8, 2022
Published: 31.01.2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 319, Pages 110–123
DOI: https://doi.org/10.1134/S0081543822050108
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: M. I. Dyachenko, S. Yu. Tikhonov, “Piecewise General Monotone Functions and the Hardy–Littlewood Theorem”, Approximation Theory, Functional Analysis, and Applications, Collected papers. On the occasion of the 70th birthday of Academician Boris Sergeevich Kashin, Trudy Mat. Inst. Steklova, 319, Steklov Math. Inst., Moscow, 2022, 120–133; Proc. Steklov Inst. Math., 319 (2022), 110–123
Citation in format AMSBIB
\Bibitem{DyaTik22}
\by M.~I.~Dyachenko, S.~Yu.~Tikhonov
\paper Piecewise General Monotone Functions and the Hardy--Littlewood Theorem
\inbook Approximation Theory, Functional Analysis, and Applications
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Boris Sergeevich Kashin
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 319
\pages 120--133
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4255}
\crossref{https://doi.org/10.4213/tm4255}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4563389}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 319
\pages 110--123
\crossref{https://doi.org/10.1134/S0081543822050108}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85148635789}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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