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FRACTIONAL FOCK–SOBOLEV SPACES

  • HONG RAE CHO (a1) and SOOHYUN PARK (a2)

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.

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

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FRACTIONAL FOCK–SOBOLEV SPACES

  • HONG RAE CHO (a1) and SOOHYUN PARK (a2)

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