Weighted inequalities for convolutions

Andersen, Kenneth F.

doi:10.1090/S0002-9939-1995-1277088-X

Weighted inequalities for convolutions
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by Kenneth F. Andersen

Proc. Amer. Math. Soc. 123 (1995), 1129-1136

DOI: https://doi.org/10.1090/S0002-9939-1995-1277088-X

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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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