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Weighted Lorentz Spaces and the Hardy Operator

✍ Scribed by M.J. Carro; J. Soria

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
389 KB
Volume
112
Category
Article
ISSN
0022-1236

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✦ Synopsis

We find a new expression for the norm of a function in the weighted Lorentz space, with respect to the distribution function, and obtain as a simple consequence a generalization of the classical embeddings (L^{r, 1} \subset \cdots \subset L^{p} \subset \cdots \subset L^{p . r}) and a new definition of the weak space (A_{i i}^{p,}\left(w^{\prime}\right)). We also give some applications to the boundedness of the Hardy operator (S f=\int_{0}^{2} f) from (A_{u_{1}}^{p_{0}}\left(w_{10}\right)) into (A_{u_{1}}^{p_{1}}\left(w_{1}\right)) with (0<p_{0} \leqslant p_{1} . \quad) " 1993 Academic Press. Inc

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