Weighted weak-type (1,1) estimates via Rubio de Francia extrapolation
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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are well known. When {Ij}j∈Z is the collection of dyadic intervals, i.e., I0 = {0} and Ij = sgn(j)[2 , 2) for |j| > 0, the estimate (1.2) is the classical Littlewood–Paley inequality which is valid (as well as the reverse estimate with ≥ in place of ≤) for all p ∈ (1,∞). If the Ij are disjoint intervals of equal length, then (1.2) holds if and only if p ∈ [2,∞); this was first proved by L. Carl...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2015
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2015.06.005