Hardy spaces associated to operators satisfying Davies–Gaffney estimates and bounded holomorphic functional calculus☆
Hardy spaces associated to operators satisfying Davies–Gaffney estimates and bounded holomorphic functional calculus☆
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DOI：
10.1016/j.jfa.2013.01.006
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发表时间：
2013-03
影响因子：
1.7
通讯作者：
X. Duong;Ji Li
中科院分区：
文献类型：
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作者：
X. Duong;Ji Li
设 X 是齐次类型的空间。假设算子 L 在 L2(X) 上具有有界全纯泛函计算，并且热半群的核 [公式：参见文本] 满足 Davies-Gaffney 估计。在不假设 L 是自伴的情况下，我们发展了 Hardy 空间 HLp(X), 0<p⩽1 的理论，其中包括分子分解、原子分解、平方函数表征、Hardy 和 Lipschitz 空间的对偶性以及 Marcinkiewicz 型插值定理。作为应用，我们证明对于所有 p>0，L 在 HLp(X) 上具有有界全纯泛函计算，并且对于所有 0<p⩽2，与 L 相关的某些 Riesz 变换从 HLp(X) 到 Lp(X) 有界。
Let X be a space of homogeneous type. Assume that an operator L has a bounded holomorphic functional calculus on L2(X) and the kernel of the heat semigroup [Formula: see text] satisfies the Davies–Gaffney estimates. Without the assumption that L is self-adjoint, we develop a theory of Hardy spaces HLp(X), 0<p⩽1, which includes a molecular decomposition, an atomic decomposition, a square function characterization, duality of Hardy and Lipschitz spaces, and a Marcinkiewicz type interpolation theorem. As applications, we show that L has a bounded holomorphic functional calculus on HLp(X) for all p>0 and certain Riesz transforms associated to L are bounded from HLp(X) to Lp(X) for all 0<p⩽2.