Weighted BMO spaces associated to operators

The Anh Bui; Xuan Thinh Duong

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arXiv · 1201.5828

Weighted BMO spaces associated to operators

The Anh Bui·Xuan Thinh Duong

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Abstract

Let $X$ be a metric space equipped with a metric $d$ and a nonnegative Borel measure $μ$ 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\}$. We show that for these spaces, the weighted John-Nirenberg inequality holds and we establish an interpolation theorem in scale of weighted $L^p$ spaces. As applications, we prove the boundedness of two singular integrals with non-smooth kernels on the weighted BMO space BMO$_\mathcal{A}(X,w)$.

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The Anh Bui, Xuan Thinh Duong. 2013-03-26. Weighted BMO spaces associated to operators. https://arxiv.org/abs/1201.5828

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