منابع مشابه
Scalar and Vector Muckenhoupt Weights
We inspect the relationship between the Ap,q condition for families of norms on vector valued functions and the Ap condition for scalar weights. In particular we will show if we are considering a norm-valued function ρ(·) such that, uniformly in all nonzero vectors x, ρ(·)(x) p ∈ Ap and ρ(·)(x) ∈ Aq then the following hold: If p = q = 2, and functions take values in R then ρ ∈ A2,2. If p = q = ...
متن کاملParaexponentials, Muckenhoupt Weights, and Resolvents of Paraproducts
We analyze the stability of Muckenhoupt’s RHdp and A d p classes of weights under a nonlinear operation, the λ-operation. We prove that the dyadic doubling reverse Hölder classes RHdp are not preserved under the λ-operation, but the dyadic doubling Ap classes A d p are preserved for 0 < λ < 1. We give an application to the structure of resolvent sets of dyadic paraproduct operators.
متن کاملEntropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, II. General weights.∗
We study compact embeddings for weighted spaces of Besov and TriebelLizorkin type where the weights belong to Muckenhoupt Ap classes. We focus our attention on the influence of singular points of the weights on the compactness of the embeddings as well as on the asymptotic behaviour of their entropy and approximation numbers.
متن کاملToeplitz Operators with Pc Symbols on General Carleson Jordan Curves with Arbitrary Muckenhoupt Weights
We describe the spectra and essential spectra of Toeplitz operators with piecewise continuous symbols on the Hardy space Hp(Γ, ω) in case 1 < p <∞, Γ is a Carleson Jordan curve and ω is a Muckenhoupt weight in Ap(Γ). Classical results tell us that the essential spectrum of the operator is obtained from the essential range of the symbol by filling in line segments or circular arcs between the en...
متن کاملA New Characterization of the Muckenhoupt Ap Weights Through an Extension of the Lorentz-Shimogaki Theorem
Given any quasi-Banach function space X over Rn it is defined an index αX that coincides with the upper Boyd index ᾱX when the space X is rearrangement-invariant. This new index is defined by means of the local maximal operator mλf . It is shown then that the Hardy-Littlewood maximal operator M is bounded on X if and only if αX < 1 providing an extension of the classical theorem of Lorentz and ...
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2013
ISSN: 0022-2518
DOI: 10.1512/iumj.2013.62.4971