Functions of vanishing mean oscillation associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates

The Anh Bui

doi:10.2748/tmj/1404911863

Functions of vanishing mean oscillation associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates

The Anh Bui^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Let L be a nonnegative self-adjoint operator satisfying Davies-Gaffney estimates on L²(X), where X is a metric space. In this paper, we introduce and develop a new function space VMO_L(X) of vanishing mean oscillation type associated to L. We then prove that the dual of VMO _L(X) is the Hardy space H_L(X) which was investigated in [18]. Some characterizations of VMO_L(X) are also established.

Original language	English
Pages (from-to)	269-287
Number of pages	19
Journal	Tohoku Mathematical Journal
Volume	66
Issue number	2
DOIs	https://doi.org/10.2748/tmj/1404911863
Publication status	Published - 2014

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title = "Functions of vanishing mean oscillation associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates",

abstract = "Let L be a nonnegative self-adjoint operator satisfying Davies-Gaffney estimates on L2(X), where X is a metric space. In this paper, we introduce and develop a new function space VMOL(X) of vanishing mean oscillation type associated to L. We then prove that the dual of VMO L(X) is the Hardy space HL(X) which was investigated in [18]. Some characterizations of VMOL(X) are also established.",

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AU - Bui, The Anh

PY - 2014

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N2 - Let L be a nonnegative self-adjoint operator satisfying Davies-Gaffney estimates on L2(X), where X is a metric space. In this paper, we introduce and develop a new function space VMOL(X) of vanishing mean oscillation type associated to L. We then prove that the dual of VMO L(X) is the Hardy space HL(X) which was investigated in [18]. Some characterizations of VMOL(X) are also established.

AB - Let L be a nonnegative self-adjoint operator satisfying Davies-Gaffney estimates on L2(X), where X is a metric space. In this paper, we introduce and develop a new function space VMOL(X) of vanishing mean oscillation type associated to L. We then prove that the dual of VMO L(X) is the Hardy space HL(X) which was investigated in [18]. Some characterizations of VMOL(X) are also established.

UR - https://www.scopus.com/pages/publications/84903943289

U2 - 10.2748/tmj/1404911863

DO - 10.2748/tmj/1404911863

M3 - Article

AN - SCOPUS:84903943289

SN - 0040-8735

VL - 66

SP - 269

EP - 287

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

IS - 2

ER -

Functions of vanishing mean oscillation associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates

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