weighted fock spaces
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2021 ◽  
Vol 15 (2) ◽  
Author(s):  
Luis Alberto Escudero ◽  
Antti Haimi ◽  
José Luis Romero

AbstractWe characterize sampling and interpolating sets with derivatives in weighted Fock spaces on the complex plane in terms of their weighted Beurling densities.


2020 ◽  
Vol 126 (3) ◽  
pp. 593-602
Author(s):  
Aamena Al-Qabani ◽  
Titus Hilberdink ◽  
Jani A. Virtanen

We study the Fredholm properties of Toeplitz operators acting on doubling Fock Hilbert spaces, and describe their essential spectra for bounded symbols of vanishing oscillation. We also compute the index of these Toeplitz operators in the special case when $\varphi (z) = \lvert {z}\rvert^{\beta }$ with $\beta >0$. Our work extends the recent results on Toeplitz operators on the standard weighted Fock spaces to the setting of doubling Fock spaces.


2019 ◽  
Vol 150 (6) ◽  
pp. 3163-3186
Author(s):  
Zhangjian Hu ◽  
Jani A. Virtanen

AbstractWe characterize Fredholmness of Toeplitz operators acting on generalized Fock spaces of the n-dimensional complex space for symbols in the space of vanishing mean oscillation VMO. Our results extend the recent characterizations for Toeplitz operators on standard weighted Fock spaces to the setting of generalized weight functions and also allow for unbounded symbols in VMO for the first time. Another novelty is the treatment of small exponents 0 < p < 1, which to our knowledge has not been seen previously in the study of the Fredholm properties of Toeplitz operators on any function spaces. We accomplish this by describing the dual of the generalized Fock spaces with small exponents.


2018 ◽  
Vol 13 (6) ◽  
pp. 2671-2686 ◽  
Author(s):  
Boo Rim Choe ◽  
Kyesook Nam

2018 ◽  
Vol 237 ◽  
pp. 79-97
Author(s):  
HONG RAE CHO ◽  
SOOHYUN PARK

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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