Quantitative Weighted Estimates for Rubio de Francia’s Littlewood–Paley Square Function
نویسندگان
چکیده
منابع مشابه
Weighted Weak-type (1, 1) Estimates via Rubio De Francia Extrapolation
The classical Rubio de Francia extrapolation result asserts that if an operator T : L0(u) → Lp0,∞(u) is bounded for some p0 > 1 and every u ∈ Ap0 , then, for every 1 < p < ∞ and every u ∈ Ap, T : L(u) → Lp,∞(u) is bounded. However, there are examples showing that it is not possible to extrapolate to the end-point p = 1. In this paper we shall prove that there exists a class of weights, slightly...
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Let Sα,ψ( f ) be the square function defined by means of the cone in R n+1 + of aperture α, and a standard kernel ψ . Let [w]Ap denote the Ap characteristic of the weight w. We show that for any 1 < p < ∞ and α ≥ 1, ‖Sα,ψ‖L p(w) αn[w] max ( 1 2 , 1 p−1 ) Ap . For each fixed α the dependence on [w]Ap is sharp. Also, on all class Ap the result is sharp in α. Previously this estimate was proved in...
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chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...
15 صفحه اولRubio de Francia’s Littlewood-Paley inequality for operator-valued functions
We prove Rubio de Francia’s Littlewood-Paley inequality for arbitrary disjoint intervals in the noncommutative setting, i.e. for functions with values in noncommutative L-spaces. As applications, we get sufficient conditions in terms of q-variation for the boundedness of Schur multipliers on Schatten classes.
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ژورنال
عنوان ژورنال: The Journal of Geometric Analysis
سال: 2019
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-019-00297-x