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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
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.
Received: June 11, 2020 Revised: October 11, 2020 Accepted: November 9, 2020
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
Linking options:
https://www.mathnet.ru/eng/tm4156https://doi.org/10.4213/tm4156 https://www.mathnet.ru/eng/tm/v312/p259
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Abstract page: | 279 | Full-text PDF : | 58 | References: | 27 | First page: | 6 |
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