Bonet Solves, José Antonio; Lusky, Wolfgang; Taskinen, Jari(Springer-Verlag, 2019-04)
[EN] Let v be a radial weight function on the unit disc or on the complex plane. It is shown that for each analytic function f0 in the Banach space Hv all analytic functions f such that v|f| is bounded, the distance of f0 ...
[EN] It is shown that the monomials A = (z(n))(n=0)(infinity) are a Schauder basis of the Frechet spaces A(+)(-gamma), gamma >= 0, that consists of all the analytic functions f on the unit disc such that (1 - vertical bar ...
Bonet Solves, José Antonio; Lusky, Wolfgang; Taskinen, J.(Elsevier, 2020-06-01)
[EN] We characterize the boundedness and compactness of Toeplitz operators T-a with radial symbols a in weighted H-infinity-spaces H(v)(infinity)on the open unit disc of the complex plane. The weights v are also assumed ...
Bonet Solves, José Antonio; Lusky, Wolfgang; Taskinen, Jari(Cambridge University Press, 2021-06)
[EN] We consider the Cauchy problem for a general class of parabolic partial differential equations in the Euclidean space R-N. We show that given a weighted L-p-space L-w(p)(R-N) with 1 <= p < infinity and a fast growing ...
Bonet Solves, José Antonio; Lusky, Wolfgang; Taskinen, Jari(Springer, 2022-09-14)
[EN] We consider weighted Bergman spaces A^1_mu on the unit disc as well as the corresponding spaces of entire functions, defined using non-atomic Borel measures with radial symmetry. By extending the techniques from the ...
Bonet Solves, José Antonio; Lusky, Wolfgang; Taskinen, Jari(Elsevier, 2021-01-01)
[EN] We prove sufficient conditions for the boundedness and compactness of Toeplitz operators T-a in weighted sup-normed Banach spaces H-v(infinity) of holomorphic functions defined on the open unit disc D of the complex ...
Bonet Solves, José Antonio; Lusky, Wolfgang; Taskinen, Jari(Springer-Verlag, 2019-09)
[EN] We consider the classical Cauchy problem for the linear heat equation and integrable initial data in the Euclidean space R-N. We show that given a weighted L-p-space L-w(p)(R-N) with 1 <= p < infinity and a fast-growing ...
Bonet Solves, José Antonio; Lusky, Wolfgang; Taskinen, Jari(Duke University Press, 2019-04)
[EN] We determine the solid hull for 2 < p < infinity and the solid core for 1 < p < 2 of weighted Bergman spaces A(mu)(p) , 1 < p < infinity, of analytic functions on the disk and on the whole complex plane, for a very ...
Bonet Solves, José Antonio; Lusky, Wolfgang; Taskinen, Jari(Springer-Verlag, 2018)
[EN] We determine the solid hull and solid core of weighted Banach spaces H-upsilon(infinity) of analytic functions functions f such that upsilon vertical bar f vertical bar is bounded, both in the case of the holomorphic ...
Bonet Solves, José Antonio; Lusky, Wolfgang; Taskinen, Jari(Springer-Verlag, 2021-12)
[EN] There are recent results concerning the boundedness and also unboundedness of Bergman projections on weighted spaces of the unit disc in special cases of rapidly decreasing weights, i.e. "large" Bergman spaces. The ...