This article is cited 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.

UDC: 517.5+517.9

Received: 29.03.2001

DOI: 10.4213/mzm473

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

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