Endpoint boundedness for multilinear commutators of Littlewood-Paley operator
نویسندگان
چکیده
منابع مشابه
Boundedness for Multilinear Commutator of Littlewood-paley Operator on Hardy and Herz-hardy Spaces
Let 0 < q < ∞ and Lqloc(R n) = {f q is locally integrable on Rn}. Suppose f ∈ Lloc(R), B = B(x0, r) = {x ∈ Rn : |x − x0| < r} denotes a ball of Rn centered at x0 and having radius r, write fB = |B|−1 ∫ B f(x)dx and f #(x) = supx∈B |B|−1 ∫ B |f(x) − fB|dx < ∞. f is said to belong to BMO(R n), if f# ∈ L∞(Rn) and define ||f ||BMO = ||f||L∞ . Let T be the Calderón-Zygmund singular integral operator...
متن کاملLipschitz Estimates for Multilinear Commutator of Littlewood-paley Operator
Let T be the Calderón-Zygmund operator, Coifman, Rochberg and Weiss (see [4]) proves that the commutator [b, T ](f) = bT (f) − T (bf)(where b ∈ BMO(R)) is bounded on L(R) for 1 < p <∞. Chanillo (see [2]) proves a similar result when T is replaced by the fractional operators. In [8, 16], Janson and Paluszynski study these results for the Triebel-Lizorkin spaces and the case b ∈ Lipβ(R), where Li...
متن کاملACTA UNIVERSITATIS APULENSIS No 19/2009 BOUNDEDNESS FOR MULTILINEAR COMMUTATOR OF LITTLEWOOD-PALEY OPERATOR ON HARDY AND HERZ-HARDY SPACES
In this paper, the (H ~b , L p) and (HK̇ q,~b , K̇ q ) type boundedness for the multilinear commutator associated with the Littlewood-paley operator are obtained.
متن کاملBoundedness of Littlewood-Paley operators and their commutators on Herz-Morrey spaces with variable exponent
The aim of this paper is to establish the vector-valued inequalities for Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley g-functions and g∗μ-functions, and their commutators on the Herz-Morrey spaces with variable exponentMK̇ p,q(·)(R n). By applying the properties of Lp(·)(Rn) spaces and the vector-valued inequalities for Littlewood-Paley operators and their...
متن کاملBoundedness for Multilinear Littlewood-Paley Operators on Hardy and Herz-Hardy Spaces
Let T be a Calderon-Zygmund operator, a classical result of Coifman, Rochberg and Weiss (see [7]) states that the commutator [b, T ] = T (bf)−bTf (where b ∈ BMO(Rn)) is bounded on Lp(Rn) for 1 < p < ∞; Chanillo (see [2]) proves a similar result when T is replaced by the fractional integral operator. However, it was observed that [b, T ] is not bounded, in general, from Hp(Rn) to Lp(Rn) for p ≤ ...
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ژورنال
عنوان ژورنال: Miskolc Mathematical Notes
سال: 2011
ISSN: 1787-2405,1787-2413
DOI: 10.18514/mmn.2011.288