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Lipschitz estimates for generalized commutators of fractional integrals with rough kernel

✍ Scribed by Shanzhen Lu; Pu Zhang

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
214 KB
Volume
252
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let $ T ^{A} _{\Omega, \alpha} $ (0 < α < n) be the generalized commutator generated by fractional integral with rough kernel and the m–th order remainder of the Taylor formula of a function A. In this paper, the (L^p^, L^r^) (r > 1) boundedness, the weak (L^1^, L^n/(n–α–β)^) boundedness and the (L^p^, Ḟ^β, ∞^~p~) boundedness of $ T ^{A} _{\Omega, \alpha} $ are discussed, when D^γ^A belongs to the Lipschitz function spaces.

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