March 18, 2024Open Access

Convolution operators and variable Hardy spaces on the Heisenberg group

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Abstract

Let H^n be the Heisenberg group. For 0 < Q=2n+2 and N N we consider exponent functions p (): H^n (0, +), which satisfies H\"older conditions, such that QQ+N < p- p () p+ < Q. In this article we prove the H^p () (H^n) L^q () (H^n) and H^p () (H^n) H^q () (H^n) boundedness of convolution operators with kernels of type (, N) on H^n, where 1q () = 1p () - Q. In particular, the Riesz potential on H^n satisfies such estimates.

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Pablo Rocha (Mon,) studied this question.

synapsesocial.com/papers/68e73a7cb6db6435876b3995 https://doi.org/https://doi.org/10.48550/arxiv.2403.11467

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