Abstract
We will obtain the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley𝒢-function, and𝒢λ*-function on the weighted Herz spacesK˙qα,p(w1,w2)(Kqα,p(w1,w2))with general weights.
Highlights
Introduction and Main ResultsLet Rn++1 = Rn × (0, ∞) and φt(x) = t−nφ(x/t)
(d) A measurable function f(x) on Rn is said to belong to the nonhomogeneous weighted weak Herz space WKqα,p(w1, w2) if
The main purpose of this paper is to consider the boundedness of intrinsic square functions on weighted Herz spaces with Ap weights
Summary
(cn)(t/(t2 + |x|2)(n+1)/2) denotes the Poisson we define the classical square function kernel (Lusin area integral) S(f) by (see [1, 2]). In [8], Wilson showed the following weighted Lp boundedness of the intrinsic square functions. (c) A measurable function f(x) on Rn is said to belong to the homogeneous weighted weak Herz space WKqα,p(w1, w2) if. (d) A measurable function f(x) on Rn is said to belong to the nonhomogeneous weighted weak Herz space WKqα,p(w1, w2) if sup λ(∑[w1. The main purpose of this paper is to consider the boundedness of intrinsic square functions on weighted Herz spaces with Ap weights. Gβ is bounded on Kqα,p(w1, w2)(Kqα,p(w1, w2)) provided that w1 and w2 satisfy either of the following: Corollary 8.
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