Vector A₂ weights and a Hardy-Littlewood maximal function

2001/01/05 by Michael Christ, Michael Goldberg · 7 citations
Mathematics · #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods #Holomorphic and Operator Theory

paper · pdf · doi:10.1090/s0002-9947-01-02759-3

Abstract

An analogue of the Hardy-Littlewood maximal function is introduced, for functions taking values in finite-dimensional Hilbert spaces. It is shown to be L² bounded with respect to weights in the class A₂ of Treil, thereby extending a theorem of Muckenhoupt from the scalar to the vector case.

Citations

• Weighted norm inequalities for the conjugate function and Hilbert transform

Cited by

• Matrix-weighted Besov spaces
• Matrix weighted norm inequalities for commutators and paraproducts with matrix symbols
• Matrix-weighted Besov-type and Triebel–Lizorkin-type spaces I: A_p-dimensions of matrix weights and φ-transform characterizations
• On off-diagonal operators in matrix-weighted spaces
• Matrix weighted estimates on spaces of homogeneous type
• Matrix-Weighted Campanato Spaces: Duality and Calderón--Zygmund Operators
• Recent results on matrix weighted norm inequalities

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