Lp-BOUNDEDNESS OF THE CAUCHY-LERAY-FANTAPPIÈ INTEGRAL ON CERTAIN CLASS OF WEAKLY PSEUDOCONVEX DOMAINS IN C2

Ly Kim Ha; Pham Huu Trung

doi:10.4134/BKMS.b240025

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Lp-BOUNDEDNESS OF THE CAUCHY-LERAY-FANTAPPIÈ INTEGRAL ON CERTAIN CLASS OF WEAKLY PSEUDOCONVEX DOMAINS IN C2

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pseudoconvex domains homogeneous spaces Cauchy-Leray-Fantappiè integral T1-theorem

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초록

Let $\mathbb{H}_k=\{(z_1,z_2) \in \mathbb{C}^2 : \operatorname{Im}z_2 > \vert z_1 \vert^{2k}\}$, for $k\in\mathbb{N}, k\ge 2$. In this paper we are interested in the $L^p$-boundedness of the Cauchy-Leray-Fantappi\`e integral. Although this operator is simpler than the Cauchy-Szeg\"o projection, it maps all $L^2(b\mathbb{H}_k)$-functions to holomorphic functions in $\mathbb{H}_k$.

Abstract

Let $\mathbb{H}_k=\{(z_1,z_2) \in \mathbb{C}^2 : \operatorname{Im}z_2 > \vert z_1 \vert^{2k}\}$, for $k\in\mathbb{N}, k\ge 2$. In this paper we are interested in the $L^p$-boundedness of the Cauchy-Leray-Fantappi\`e integral. Although this operator is simpler than the Cauchy-Szeg\"o projection, it maps all $L^2(b\mathbb{H}_k)$-functions to holomorphic functions in $\mathbb{H}_k$.

참고문헌 (15)

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