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Mat. Zametki, 2002, Volume 72, Issue 6, Pages 869–882 (Mi mz473)  

This article is cited in 1 scientific paper (total in 1 paper)

On Weighted Norms of Riesz Transforms Equal to One

E. A. Kalita

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences

Abstract: We consider the vector Riesz transform $\nabla ^t\Delta ^{-(t+s)/2}\operatorname {div}^s$ of even order $s+t$ in the weighted space$L_2(\mathbb R^n;|x|^a)$. We establish that for $t\ne s$, $n>3$ its norm is equal to one on some interval of values of $a$, while inside the interval a stronger estimate for a subordinate norm is valid.

DOI: https://doi.org/10.4213/mzm473

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English version:
Mathematical Notes, 2002, 72:6, 799–810

Bibliographic databases:

UDC: 517.5+517.9
Received: 29.03.2001

Citation: E. A. Kalita, “On Weighted Norms of Riesz Transforms Equal to One”, Mat. Zametki, 72:6 (2002), 869–882; Math. Notes, 72:6 (2002), 799–810

Citation in format AMSBIB
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\paper On Weighted Norms of Riesz Transforms Equal to One
\jour Mat. Zametki
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\pages 869--882
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\crossref{https://doi.org/10.1023/A:1021437929109}
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    This publication is cited in the following articles:
    1. “Classical Solvability of a Parabolic System of Two Nonlinear Equations”, Differ. Equ., 47:4 (2011), 593–598  crossref  mathscinet  zmath  isi  elib  scopus
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