Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Weighted inequalities for convolutions

Author: Kenneth F. Andersen
Journal: Proc. Amer. Math. Soc. 123 (1995), 1129-1136
MSC: Primary 44A10; Secondary 26D15, 44A35
MathSciNet review: 1277088
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Abstract: For certain convolution operators T on $ {R^ + }$ or $ {R^n}$, sufficient conditions are given which ensure that T is bounded between weighted Lebesgue spaces. The class of operators considered includes many of classical interest; in particular, new inequalities are obtained for the Laplace transform, the Poisson integral on $ {R^n} \times {R^ + }$, and Goldberg's transform.

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Keywords: Weighted inequalities, convolution, integral operator
Article copyright: © Copyright 1995 American Mathematical Society