578 research outputs found
Essential norms of Volterra-type operators between~~ type spaces
~In this paper, we investigate the boundedness of some Volterra-type
operators between ~~ type spaces. Then, we give the essential norms of
such operators in terms of ~, their derivatives and the n-th power
~ of ~
On an integral operator between Bloch-type spaces on the unit ball
AbstractWe characterize the boundedness and compactness of the following integral-type operatorIφg(f)(z)=∫01Rf(φ(tz))g(tz)dtt,z∈B, where g is a holomorphic function on the unit ball B⊂Cn such that g(0)=0, and φ is a holomorphic self-map of B, acting from α-Bloch spaces to Bloch-type spaces on B
Operators on some analytic function spaces and their dyadic counterparts
In this thesis we consider several questions on harmonic and analytic functions spaces and
some of their operators. These questions deal with Carleson-type measures in the unit
ball, bi-parameter paraproducts and multipliers problem on the bitorus, boundedness of
the Bergman projection and analytic Besov spaces in tube domains over symmetric cones.
In part I of this thesis, we show how to generate Carleson measures from a class of
weighted Carleson measures in the unit ball. The results are used to obtain boundedness
criteria of the multiplication operators and Ces`aro integral-type operators between
weighted spaces of functions of bounded mean oscillation in the unit ball.
In part II of this thesis, we introduce a notion of functions of logarithmic oscillation
on the bitorus. We prove using Cotlar’s lemma that the dyadic version of the set of
such functions is the exact range of symbols of bounded bi-parameter paraproducts on the
space of functions of dyadic bounded mean oscillation. We also introduce the little space of
functions of logarithmic mean oscillation in the same spirit as the little space of functions of
bounded mean oscillation of Cotlar and Sadosky. We obtain that the intersection of these
two spaces of functions of logarithmic mean oscillation and L1 is the set of multipliers of
the space of functions of bounded mean oscillation in the bitorus.
In part III of this thesis, in the setting of the tube domains over irreducible symmetric
cones, we prove that the Bergman projection P is bounded on the Lebesgue space Lp if
and only if the natural mapping of the Bergman space Ap0 to the dual space (Ap) of
the Bergman space Ap, where 1
p + 1
p0 = 1, is onto. On the other hand, we prove that for
p > 2, the boundedness of the Bergman projection is also equivalent to the validity of an
Hardy-type inequality. We then develop a theory of analytic Besov spaces in this setting
defined by using the corresponding Hardy’s inequality. We prove that these Besov spaces
are the exact range of symbols of Schatten classes of Hankel operators on the Bergman
space A2
Carleson measures, Riemann-Stieltjes and multiplication operators on a general family of function spaces
Let be a nonnegative Borel measure on the unit disk of the complex
plane. We characterize those measures such that the general family of
spaces of analytic functions, , which contain many classical function
spaces, including the Bloch space, and the spaces, are embedded
boundedly or compactly into the tent-type spaces . The
results are applied to characterize boundedness and compactness of
Riemann-Stieltjes operators and multiplication operators on .Comment: 26 page
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