THE LOCAL NON-HOMOGENEOUS Tb THEOREM FOR VECTOR-VALUED FUNCTIONS

DOI10.1017/S0017089514000123zbMath1320.42011arXiv1201.0648OpenAlexW2963254441WikidataQ110020200 ScholiaQ110020200MaRDI QIDQ2940226

Antti V. Vähäkangas, Tuomas P. Hytönen

Publication date: 26 January 2015

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.0648

zbMATH Keywords

singular integralsvector-valued functionsUMD spacesBanach function latticeCalderón-Zygmund operatornon-doubling measure

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Spaces of vector- and operator-valued functions (46E40) Martingales and classical analysis (60G46)

Related Items (6)

Boundedness of the square function and rectifiability ⋮ A decomposition theorem for singular integral operators on spaces of homogeneous type ⋮ The perfect local $Tb$ Theorem and twisted Martingale transforms ⋮ On pointwise \(\ell^r\)-sparse domination in a space of homogeneous type ⋮ Vector-valued extensions of operators through multilinear limited range extrapolation ⋮ The local \(Tb\) theorem with rough test functions

Cites Work

• Some remarks on Banach spaces in which martingale difference sequences are unconditional
• Boundedness of the square function and rectifiability
• Accretive system \(Tb\)-theorems on nonhomogeneous spaces.
• The \(Tb\)-theorem on non-homogeneous spaces.
• Non-homogeneous \(Tb\) theorem and random dyadic cubes on metric measure spaces
• Kato's square root problem in Banach spaces
• On the relation of Carleson's embedding and the maximal theorem in the context of Banach space geometry
• On the Rademacher maximal function
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
• Operator-valued Fourier multiplier theorems and maximal \(L_p\)-regularity

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