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FRACTIONAL FOCK–SOBOLEV SPACES

Published online by Cambridge University Press:  06 March 2018

HONG RAE CHO
Affiliation:
Department of Mathematics, Pusan National University, Pusan 609-735, Republic of Korea email [email protected]
SOOHYUN PARK
Affiliation:
Department of Mathematics, Pusan National University, Pusan 609-735, Republic of Korea email [email protected]

Abstract

Let $s\in \mathbb{R}$ and $0<p\leqslant \infty$. The fractional Fock–Sobolev spaces $F_{\mathscr{R}}^{s,p}$ are introduced through the fractional radial derivatives $\mathscr{R}^{s/2}$. We describe explicitly the reproducing kernels for the fractional Fock–Sobolev spaces $F_{\mathscr{R}}^{s,2}$ and then get the pointwise size estimate of the reproducing kernels. By using the estimate, we prove that the fractional Fock–Sobolev spaces $F_{\mathscr{R}}^{s,p}$ are identified with the weighted Fock spaces $F_{s}^{p}$ that do not involve derivatives. So, the study on the Fock–Sobolev spaces is reduced to that on the weighted Fock spaces.

Type
Article
Copyright
© 2018 Foundation Nagoya Mathematical Journal  

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Footnotes

The author was supported by NRF of Korea (NRF-2016R1D1A1B03933740).

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