Weakly Canceling Operators and Singular Integrals

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Weakly Canceling Operators and Singular Integrals. / Stolyarov, D. M.

In: Proceedings of the Steklov Institute of Mathematics, Vol. 312, No. 1, 03.2021, p. 249-260.

Research output: Contribution to journal › Article › peer-review

Author

Stolyarov, D. M. / Weakly Canceling Operators and Singular Integrals. In: Proceedings of the Steklov Institute of Mathematics. 2021 ; Vol. 312, No. 1. pp. 249-260.

BibTeX

@article{1a6d6c5eb66b43bd88a064d2c361f205,

title = "Weakly Canceling Operators and Singular Integrals",

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 parallel to f parallel to(L infinity) less than or similar to parallel to Af parallel to(L1) if A is a weakly canceling operator of order d and the inequality parallel to f parallel to(L2) less than or similar to parallel to Af parallel to(L1) if A is a canceling operator of order d/2, provided f is a function of d variables.",

keywords = "VECTOR-FIELDS, EQUATIONS",

author = "Stolyarov, {D. M.}",

note = "Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = mar,

doi = "10.1134/S0081543821010168",

language = "English",

volume = "312",

pages = "249--260",

journal = "Proceedings of the Steklov Institute of Mathematics",

issn = "0081-5438",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "1",

}

RIS

TY - JOUR

T1 - Weakly Canceling Operators and Singular Integrals

AU - Stolyarov, D. M.

PY - 2021/3

Y1 - 2021/3

N2 - 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 parallel to f parallel to(L infinity) less than or similar to parallel to Af parallel to(L1) if A is a weakly canceling operator of order d and the inequality parallel to f parallel to(L2) less than or similar to parallel to Af parallel to(L1) if A is a canceling operator of order d/2, provided f is a function of d variables.

AB - 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 parallel to f parallel to(L infinity) less than or similar to parallel to Af parallel to(L1) if A is a weakly canceling operator of order d and the inequality parallel to f parallel to(L2) less than or similar to parallel to Af parallel to(L1) if A is a canceling operator of order d/2, provided f is a function of d variables.

KW - VECTOR-FIELDS

KW - EQUATIONS

UR - http://www.scopus.com/inward/record.url?scp=85105925479&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/86ebc0fc-6104-3e29-8ea8-a24f6c5b0c49/

U2 - 10.1134/S0081543821010168

DO - 10.1134/S0081543821010168

M3 - Article

AN - SCOPUS:85105925479

VL - 312

SP - 249

EP - 260

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - 1

ER -

ID: 88986254