Sharp estimates for the Bochner-Riesz operator of negative order in

Author:
Jong-Guk Bak

Journal:
Proc. Amer. Math. Soc. **125** (1997), 1977-1986

MSC (1991):
Primary 42B15

DOI:
https://doi.org/10.1090/S0002-9939-97-03723-4

MathSciNet review:
1371114

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Abstract | References | Similar Articles | Additional Information

Abstract: The Bochner-Riesz operator on of order is defined by

where denotes the Fourier transform and if , and if . We determine all pairs such that on of negative order is bounded from to . To be more precise, we prove that for the estimate holds if and only if , where

We also obtain some weak-type results for .

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Additional Information

**Jong-Guk Bak**

Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306–3027

Address at time of publication:
Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Korea

Email:
bak@euclid.postech.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-97-03723-4

Received by editor(s):
October 3, 1995

Received by editor(s) in revised form:
December 19, 1995

Additional Notes:
The author’s research was partially supported by a grant from the Pohang University of Science and Technology

Communicated by:
Christopher D. Sogge

Article copyright:
© Copyright 1997
American Mathematical Society