The UMD conjecture is reduced to L^p boundedness of a pair of simple dyadic shift operators via equivalence with the Hilbert transform.
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Introduces the matrix-weighted variable Hardy space H^{p(·)}_W and establishes its atomic characterization along with applications to dual spaces and Calderón-Zygmund operator boundedness.
Defines variable A_{p(·),∞} weights and shows they are equivalent to the reverse Hölder condition in variable Lebesgue spaces, with matrix versions and dimension estimates for reducing operators.
Martingale square functions with matrix weights satisfy L_p bounds characterized by matrix A_p conditions, with sharpness for 1<p≤2 and optimal exponents achieved in the scalar case for all 1<p<∞.
citing papers explorer
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A twosided linear estimate and a dyadic reduction of the UMD Conjecture
The UMD conjecture is reduced to L^p boundedness of a pair of simple dyadic shift operators via equivalence with the Hilbert transform.
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Atomic Characterization and Its Applications of Matrix-Weighted Variable Hardy Spaces
Introduces the matrix-weighted variable Hardy space H^{p(·)}_W and establishes its atomic characterization along with applications to dual spaces and Calderón-Zygmund operator boundedness.
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Variable Muckenhoupt $A_\infty$ Weights
Defines variable A_{p(·),∞} weights and shows they are equivalent to the reverse Hölder condition in variable Lebesgue spaces, with matrix versions and dimension estimates for reducing operators.
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Sharp weighted norm estimates for martingale square functions
Martingale square functions with matrix weights satisfy L_p bounds characterized by matrix A_p conditions, with sharpness for 1<p≤2 and optimal exponents achieved in the scalar case for all 1<p<∞.