Characterization of temperatures associated to Schrodinger operators with initial data in BMO spaces

Minghua Yang; Chao Zhang

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arXiv · 1710.01160

Characterization of temperatures associated to Schrodinger operators with initial data in BMO spaces

Minghua Yang·Chao Zhang

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Abstract

Let L be a Schr\"odinger operator of the form L=-\Delta+V acting on L^2(\mathbb R^n) where the nonnegative potential V belongs to the reverse H\"older class B_q for some q>= n. Let BMO denote the BMO space associated to the Schr\"odinger operator L. In this article we will show that a function f in BMO_L is the trace of the solution of u_t+L u=0, u(x,0)= f(x), where u satisfies a Carleson-type condition. Conversely, this Carleson condition characterizes all the L-carolic functions whose traces belong to the space BMO_L. This result extends the analogous characterization founded by Fabes and Neri for the classical BMO space of John and Nirenberg.

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Minghua Yang, Chao Zhang. 2017-10-02. Characterization of temperatures associated to Schrodinger operators with initial data in BMO spaces. https://arxiv.org/abs/1710.01160

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