REVIEW 4 cited by
New Characterizations and Properties of Matrix $A_\infty$ Weights
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
We provide several new characterizations of $A_{p,\infty}$-matrix weights, originally introduced by A. Volberg as matrix-valued substitutes of the classical $A_\infty$ weights. In analogy with the notion of $A_p$-dimension of matrix weights introduced in our previous work, we introduce the concepts of the lower and the upper dimensions of $A_{p,\infty}$-matrix weights, which enable us to obtain sharp estimates related to their reducing operators. In a follow-up work, these results will play a key role in the study of function spaces with $A_{p,\infty}$-matrix weights, which extends earlier results in the more restricted class of $A_p$-matrix weights.
Forward citations
Cited by 4 Pith papers
-
Maximal Function and Atomic Characterizations of Matrix-Weighted Hardy Spaces with Their Applications to Boundedness of Calder\'on--Zygmund Operators
For p≤1 and A_p matrix weights, matrix-weighted Hardy spaces admit maximal-function, atomic, finite-atomic, and Calderón–Zygmund operator characterizations.
-
Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding
Generalized matrix-weighted Besov-Triebel-Lizorkin spaces with growth functions are fully characterized (phi-transform, maximal functions, molecules, wavelets), and p-invariance holds iff the matrix weight is eigenval...
-
Besov--Triebel--Lizorkin-Type Spaces with Matrix $A_\infty$ Weights
Matrix A-infinity weighted Besov and Triebel-Lizorkin type spaces are characterized via phi-transforms, molecules, wavelets, and atoms, with sharp boundedness conditions for almost diagonal and classical operators.
-
Matrix-Weighted Besov--Triebel--Lizorkin Spaces of Optimal Scale: Boundedness of Pseudo-Differential, Trace, and Calder\'{o}n--Zygmund Operators
Pseudo-differential, trace, extension, and Calderon-Zygmund operators are shown to be bounded on generalized matrix-weighted Besov-Triebel-Lizorkin-type spaces with matrix A-infinity weights.
Discussion (0). Continue with ORCID to comment.