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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 312, Pages 259–271
DOI: https://doi.org/10.4213/tm4156
(Mi tm4156)
 

This article is cited in 3 scientific papers (total in 3 papers)

Weakly Canceling Operators and Singular Integrals

D. M. Stolyarov

Department of Mathematics and Computer Science, St. Petersburg State University, Line 14 (Vasilyevsky Island), 29, St. Petersburg, 199178 Russia
Full-text PDF (239 kB) Citations (3)
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Abstract: We suggest an elementary harmonic analysis approach to canceling and weakly canceling differential operators, which allows us to extend these notions to the anisotropic setting and replace differential operators with Fourier multiplies with mild smoothness regularity. In this more general setting of anisotropic Fourier multipliers, we prove the inequality $\|f\|_{L_\infty } \lesssim \|Af\|_{L_1}$ if $A$ is a weakly canceling operator of order $d$ and the inequality $\|f\|_{L_2} \lesssim \|Af\|_{L_1}$ if $A$ is a canceling operator of order $d/2$, provided $f$ is a function of $d$ variables.
Funding agency Grant number
Russian Science Foundation 19-71-30002
This work is supported by the Russian Science Foundation under grant 19-71-30002.
Received: June 11, 2020
Revised: October 11, 2020
Accepted: November 9, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 312, Pages 249–260
DOI: https://doi.org/10.1134/S0081543821010168
Bibliographic databases:
Document Type: Article
UDC: 517.983.37
Language: Russian
Citation: D. M. Stolyarov, “Weakly Canceling Operators and Singular Integrals”, Function Spaces, Approximation Theory, and Related Problems of Analysis, Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 312, Steklov Math. Inst., Moscow, 2021, 259–271; Proc. Steklov Inst. Math., 312 (2021), 249–260
Citation in format AMSBIB
\Bibitem{Sto21}
\by D.~M.~Stolyarov
\paper Weakly Canceling Operators and Singular Integrals
\inbook Function Spaces, Approximation Theory, and Related Problems of Analysis
\bookinfo Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 312
\pages 259--271
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4156}
\crossref{https://doi.org/10.4213/tm4156}
\elib{https://elibrary.ru/item.asp?id=46066119}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 312
\pages 249--260
\crossref{https://doi.org/10.1134/S0081543821010168}
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  • https://doi.org/10.4213/tm4156
  • https://www.mathnet.ru/eng/tm/v312/p259
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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