Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces

• Autorzy: Sergio Antonio Tozoni
• Języki publikacji: EN

Abstrakty

EN

Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis $(e_{j})_{j≥1}$. Given an operator T from $L^{∞}_{c}(X)$ to L¹(X), we consider the vector-valued extension T̃ of T given by $T̃(∑_{j} f_{j}e_{j}) = ∑_{j} T(f_{j})e_{j}$. We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient conditions on the kernel of a singular integral operator to have the boundedness of the vector-valued extension of this operator on $L^{p}(X,Wdμ;E)$ for 1 < p < ∞ and for a weight W in the Muckenhoupt class $A_{p}(X)$. Applications to singular integral operators on the unit sphere Sⁿ and on a finite product of local fields 𝕂ⁿ are given. The versions of all these results for vector-valued extensions of operators on functions defined on a homogeneous space X and with values in a UMD Banach lattice are also given.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 60G46: Martingales and classical analysis
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 161
• Numer: 1
• Strony: 71-97

Daty

wydano

2004

Twórcy

autor

Sergio Antonio Tozoni

• Instituto de Matemática, Universidade Estadual de Campinas, Caixa Postal 6065, 13.081-970 Campinas - SP, Brazil

Identyfikatory

DOI

10.4064/sm161-1-5