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. The fractional Fock–Sobolev spaces
are introduced through the fractional radial derivatives
. We describe explicitly the reproducing kernels for the fractional Fock–Sobolev spaces
and then get the pointwise size estimate of the reproducing kernels. By using the estimate, we prove that the fractional Fock–Sobolev spaces
are identified with the weighted Fock spaces
that do not involve derivatives. So, the study on the Fock–Sobolev spaces is reduced to that on the weighted Fock spaces.
Let Ψ ∈ C2[0,1] be a positive real valued function on (0, 1]. Under certain assumptions on Ψ, the set is a pseudoconvex domain with C2-boundary which may be infinite type. If Ψ has flatness at 0 so that then we can obtain Lp(1 ≤ p ≤ ∞) estimates for on D.
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