Weighted BMO spaces associated to operators

Abstract

Let $X$ be a metric space equipped with a metric $d$ and a nonnegative Borel measure $\mu$ satisfying the doubling property and let $\{{\mathcal{A}}_t{\}}_{t>0}$, be a generalized approximations to the identity, for example $\{{\mathcal{A}}_t\}$ is a holomorphic semigroup $e^{-tL}$ with Gaussian upper bounds generated by an operators $L$ on $L^2(X)$. In this paper, we introduce and study the weighted BMO space BMO${}_{\mathcal{A}}(X,w)$ associated to the the family \{\mathcal{A}_t\}$.Weshowthatforthesespaces,theweightedJohn-Nirenberginequalityholdsandweestablishaninterpolationtheoreminscaleofweighted$L^p$spaces.Asapplications,weprovetheboundednessoftwosingularintegralswithnon-smoothkernelsontheweightedBMOspaceBMO$_\mathcal{A}(X,w)$.

In this version, the results on Hardy spaces were removed

References in corpus (1)

• Weighted Hardy spaces associated to operators and boundedness of singular integrals

Cited by in corpus (2)

• Weighted Besov and Triebel--Lizorkin spaces associated to operators
• Musielak-Orlicz BMO-Type Spaces Associated with Generalized Approximations to the Identity