Preduals of quadratic Campanato spaces associated to operators with heat kernel bounds

2014/02/24 by Liang Song, Jie Xiao, Song, Liang +3
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1402.5717

openalex publication_date 2014/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L be a nonnegative, self-adjoint operator on L²(ℝⁿ) with the Gaussian upper bound on its heat kernel. As a generalization of the square Campanato space L^2,λ_-Δ(\mathbb Rⁿ), in \citeDXY the quadratic Campanato space L_L^2,λ(ℝⁿ) is defined by a variant of the maximal function associated with the semigroup \e^-tL\_{t≥ 0}. On the basis of \citeDX and \citeYY this paper addresses the preduality of L_L^2,λ(ℝⁿ) through an induced atom (or molecular) decomposition. Even in the case L=-Δ the discovered predual result is new and natural.

Citations

• Some new function spaces and their applications to Harmonic analysis
• On the solutions of quasi-linear elliptic partial differential equations

Related

• A maximal function characterization for Hardy spaces associated to nonnegative self-adjoint operators satisfying Gaussian estimates
• Maximal Function Characterizations of Musielak-Orlicz-Hardy Spaces Associated to Non-negative Self-adjoint Operators Satisfying Gaussian Estimates
• Atomic and Maximal Function Characterizations of Musielak-Orlicz-Hardy Spaces Associated to Non-negative Self-adjoint Operators on Spaces of Homogeneous Type
• The Garnett-Jones Theorem on BMO spaces associated with operators and applications
• Restriction estimates via the derivatives of the heat semigroup and connexion with dispersive estimates