721 research outputs found
Meromorphic Bergman spaces
In this paper we introduce new spaces of holomorphic functions on the pointed
unit disc of that generalize classical Bergman spaces. We prove
some fundamental properties of these spaces and their dual spaces. We finish
the paper by extending Hardy-Littlewood and Fej\'er-Riesz inequalities to these
spaces with an application on Toeplitz operators.Comment: 15 pages, no figur
Hardy’s inequality for functions of several complex variables
We obtain a generalization of Hardy’s inequality for functions in the Hardy space H1 (Bd), where Bd is the unit ball
{z = (z1, …, zd) ∈ In particular, we construct a function φ on the set of d –dimensional multi-indices
{n = (n1, …, nd) | ni ∈ {0}} and prove that if f(z) = Σ anzn is a function in H1 (Bd), then ≤ Moreover, our proof shows that this inequality is also valid for functions in Hardy space on the polydisk H1 (Bd)
Volterra-type inner derivations on Hardy spaces
A classical result of Calkin [Ann. of Math. (2) 42 (1941), pp. 839-873] says
that an inner derivation maps the algebra of bounded
operators on a Hilbert space into the ideal of compact operators if and only if
is a compact perturbation of the multiplication by a scalar. In general, an
analogous statement fails for operators on Banach spaces. To complement
Calkin's result, we characterize Volterra-type inner derivations on Hardy
spaces using generalized area operators and compact intertwining relations for
Volterra and composition operators. Further, we characterize the compact
intertwining relations for multiplication and composition operators between
Hardy and Bergman spaces
The Corona Theorem for the Drury-Arveson Hardy space and other holomorphic Besov-Sobolev spaces on the unit ball in
We prove that the multiplier algebra of the Drury-Arveson Hardy space
on the unit ball in has no corona in its maximal
ideal space, thus generalizing the famous Corona Theorem of L. Carleson to
higher dimensions. This result is obtained as a corollary of the Toeplitz
corona theorem and a new Banach space result: the Besov-Sobolev space
has the "baby corona property" for all and
. In addition we obtain infinite generator and semi-infinite
matrix versions of these theorems.Comment: v1: 70 pgs; v2: 73 pgs.; introduction expanded, clarified. v3: 73
pgs.; restriction in main result removed (see 9.2), arguments expanded (see
8.1.1). v4: 74 pgs.; systematic arithmetic misprints fixed on pgs. 37-48. v5:
76 pgs.; incorrect embedding corrected via Proposition 4. v6: 80 pgs.; main
result extended to vector-valued setting. v7: 82 pgs.; typos removed
Asymptotic results on modified Bergman-Dirichlet spaces and examples of Segal-Bargmann transforms
In this paper, we start by introducing the modified Bergman-Dirichlet space
and then we study its
asymptotic behavior when the parameter goes to infinity and to
to obtain respectively the modified Bargmann-Dirichlet and the modified
Hardy-Dirichlet spaces with their reproducing kernels. Finally, we give some
examples of Segal-Bargmann transforms of those spaces.Comment: 19 page
Guido Weiss: a few memories of a friend and an influential mathematician
This contribution starts with an exchange between us on the way we met Guido
and he influenced our mathematical lives. Then it is mainly a survey paper that
illustrates this influence by describing different topics and their subsequent
evolution after his seminal papers and courses. Our main thread is the notion
of a space of homogeneous type. In the second section we describe how it became
central in pluricomplex analysis and consider particularly the existence of
weak factorization for spaces of holomorphic functions. In the last section,
one revisits the construction of a basis of wavelets in a space of homogeneous
type and the way it allows a Littlewood-Paley analysis
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