Maximal Function Characterizations of Variable Hardy Spaces Associated with Non-negative Self-adjoint Operators Satisfying Gaussian Estimates

2016/01/28 by Ciqiang Zhuo, Dachun Yang, Zhuo, Ciqiang +1
Mathematics · #35K08 (Secondary) #42B25 (Primary) #42B30 #42B35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1601.07615

openalex publication_date 2016/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p(⋅): \mathbb Rⁿ→(0,1] be a variable exponent function satisfying the globally log-Hölder continuous condition and L a non-negative self-adjoint operator on L²(\mathbb Rⁿ) whose heat kernels satisfying the Gaussian upper bound estimates. Let H_L^p(⋅)(\mathbb Rⁿ) be the variable exponent Hardy space defined via the Lusin area function associated with the heat kernels \e^-t2L\_{t∈ (0,∞)}. In this article, the authors first establish the atomic characterization of H_L^p(⋅)(\mathbb Rⁿ); using this, the authors then obtain its non-tangential maximal function characterization which, when p(⋅) is a constant in (0,1], coincides with a recent result by Song and Yan [Adv. Math. 287 (2016), 463-484] and further induces the radial maximal function characterization of H_L^p(⋅)(\mathbb Rⁿ) under an additional assumption that the heat kernels of L have the Hölder regularity.

Citations

• Hardy spaces with variable exponents and generalized Campanato spaces
• Some new function spaces and their applications to Harmonic analysis
• Parabolic maximal functions associated with a distribution, II

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