Fock-Sobolev Spaces of Fractional Order

Microscopic densities and Fock-Sobolev spaces

“…The space L 2 a (µ 0 ) is a kind of Fock-Sobolev space of entire functions, associated with the generalized Fock-weight Q 0 and the Sobolev parameter c. Incidentally, related spaces were introduced recently in the papers [6,7].…”

Volterra type operators on growth Fock spaces

“…This fact allows to extend most of the results of the present paper to F ∞ 1,β (C d ), β ∈ R. We restrict our attention to characterizations of q-Carleson measures for F p 1,β (C d ). For 0 < p < ∞, the problem is solved in [4]. So, we consider the case where p = ∞.…”

Sarason’s Conjecture of Toeplitz Operators on Fock-Sobolev Type Spaces

“…where { } is any orthonormal basis for 2 with respect to ⟨⋅, ⋅⟩ . Note that polynomials form a dense subset of 2 (see Proposition 2.3 in [2]). Also note that monomials are mutually orthogonal, which means that { /√⟨ , ⟩ } is an orthonormal basis for 2 .…”