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Preduals of Quadratic Campanato Spaces Associated to Operators with Heat Kernel Bounds

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Abstract

Let L be a nonnegative, self-adjoint operator on \(L^{2}(\mathbb {R}^{n})\) with the Gaussian upper bound on its heat kernel. As a generalization of the square Campanato space \(\mathcal {L}^{2,\lambda }_{-\Delta }(\mathbb R^{n})\), in Duong et al. (J. Fourier Anal. Appl. 13:87–111, 2007) the quadratic Campanato space \(\mathcal {L}_{L}^{2,\lambda }(\mathbb {R}^{n})\) is defined by a variant of the maximal function associated with the semigroup {e −tL} t≥0. On the basis of Dafni and Xiao (J. Funct. Anal. 208:377–422, 2004) and Yang and Yuan (J. Funct. Anal. 255:2760–2809, 2008) this paper addresses the preduality of \(\mathcal {L}_{L}^{2,\lambda }(\mathbb {R}^{n})\) through an induced atom (or molecular) decomposition. Even in the case L = −Δ the discovered predual result is new and natural.

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Authors and Affiliations

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China

    Liang Song & Xuefang Yan

  2. Department of Mathematics and Statistics, Memorial University, St. John’s, NL, A1C 5S7, Canada

    Jie Xiao

  3. College of Mathematics and Information Science, Heibei Normal University, Shijiazhuang, 050016, People’s Republic of China

    Xuefang Yan

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  1. Liang Song
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Correspondence to Liang Song.

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Song, L., Xiao, J. & Yan, X. Preduals of Quadratic Campanato Spaces Associated to Operators with Heat Kernel Bounds. Potential Anal 41, 849–867 (2014). https://doi.org/10.1007/s11118-014-9396-7

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