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On Weighted Hardy Spaces on Complex Semigroups

✍ Scribed by Karl-Hermann Neeb


Publisher
Springer
Year
1998
Tongue
English
Weight
326 KB
Volume
56
Category
Article
ISSN
0037-1912

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Let , be analytic functions defined on ‫,ބ‬ such that ‫ބ‬ : ‫.ބ‬ The operator Ε½ . given by f Β¬ f ( is called a weighted composition operator. In this paper we deal with the boundedness, compactness, weak compactness, and complete continu-Ε½ . ity of weighted composition operators on Hardy spaces H 1

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## Abstract Using Herz spaces, we obtain a sufficient condition for a bounded measurable function on ℝ^__n__^ to be a Fourier multiplier on __H^p^~Ξ±~__ (ℝ^__n__^ ) for 0 < __p__ < 1 and –__n__ < Ξ± ≀ 0. Our result is sharp in a certain sense and generalizes a recent result obtained by Baernstein an