BMO from dyadic BMO for nonhomogeneous measures
نویسندگان
چکیده
منابع مشابه
BMO is the intersection of two translates of dyadic BMO
Let T be the unit circle on R2. Denote by BMO(T) the classical BMO space and denote by BMOD(T) the usual dyadic BMO space on T. Then, for suitably chosen δ ∈R, we have ‖φ‖BMO(T) ‖φ‖BMOD(T) + ‖φ(· − 2δπ)‖BMOD(T), ∀φ ∈ BMO(T). To cite this article: T. Mei, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 2003 Académie des sciences. Published by Éditions scientifiques et médicales Elsevier SAS. All ri...
متن کاملBmo for Nondoubling Measures
1. Introduction. The Calderón-Zygmund theory of singular integrals has been traditionally considered with respect to a measure satisfying a doubling condition. Recently, Tolsa [T] and, independently, Nazarov, Treil, and Volberg [NTV] have shown that this standard doubling condition was not really necessary. Likewise, in the homogeneous spaces setting, functions of bounded mean oscillation, BMO,...
متن کاملOn the John-strömberg Characterization of Bmo for Nondoubling Measures
A well known result proved by F. John for 0 < λ < 1/2 and by J.-O. Strömberg for λ = 1/2 states that ‖f‖BMO(ω) sup Q inf c∈R inf{α > 0 : ω{x ∈ Q : |f(x)− c| > α} < λω(Q)} for any measure ω satisfying the doubling condition. In this note we extend this result to all absolutely continuous measures. In particular, we show that Strömberg’s “1/2-phenomenon” still holds in the nondoubling case. An im...
متن کاملBmo-boundedness of the Maximal Operator for Arbitrary Measures
We show that in the one-dimensional case the weighted Hardy–Littlewood maximal operator Mμ is bounded on BMO(μ) for arbitrary Radon measure μ, and that this is not the case in higher dimensions.
متن کاملQuasi-orthogonal expansions for functions in BMO
For {φ_n(x)}, x ε [0,1] an orthonormalsystem of uniformly bounded functions, ||φ_n||_{∞}≤ M
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Publicacions Matemàtiques
سال: 2020
ISSN: 0214-1493
DOI: 10.5565/publmat6412014