Weighted weak-type inequalities

for the maximal function of nonnegative

integral transforms over approach regions

Author:
Shiying Zhao

Journal:
Proc. Amer. Math. Soc. **125** (1997), 2013-2020

MSC (1991):
Primary 42B20, 42B25

MathSciNet review:
1372047

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Abstract | References | Similar Articles | Additional Information

Abstract: The relation between approach regions and singularities of nonnegative kernels is studied, where , , , and is a homogeneous space. For , a sufficient condition on approach regions () is given so that the maximal function

is weak-type with respect to a pair of measures and . It is shown that this condition is also necessary for operators of potential type in the sense of Sawyer and Wheedon (Amer. J. Math. **114** (1992), 813-874).

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Additional Information

**Shiying Zhao**

Affiliation:
Department of Mathematics and Computer Science, University of Missouri-St. Louis, St. Louis, Missouri 63121

Email:
zhao@greatwall.cs.umsl.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03784-2

Keywords:
Weak type inequalities,
weights,
operators of potential type,
maximal functions,
approach regions

Received by editor(s):
April 13, 1994

Received by editor(s) in revised form:
January 19, 1996

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1997
American Mathematical Society