Singular measures and convolution operators

Details Singular measures and convolution operators Singular measures and convolution operators

2002-07-30

arxiv.org/abs/math/0207285v1

Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 3, 487-490

Mathematics

Classical Analysis and ODEs

8 pages

Scientific paper

10.1007/s10114-005-0682-6

We show that in the study of certain convolution operators, functions can be
replaced by measures without changing the size of the constants appearing in
weak type (1,1) inequalities. As an application, we prove that the best
constants for the centered Hardy-Littlewood maximal operator associated to
parallelotopes do not decrease with the dimension.

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