Premium
Lipschitz estimates for generalized commutators of fractional integrals with rough kernel
Author(s) -
Lu Shanzhen,
Zhang Pu
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310038
Subject(s) - mathematics , lipschitz continuity , commutator , remainder , omega , kernel (algebra) , order (exchange) , mathematical analysis , pure mathematics , function (biology) , algebra over a field , arithmetic , lie conformal algebra , physics , finance , quantum mechanics , economics , evolutionary biology , biology
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.