The algebra property of the integrals of some analytic functions in the unit disk.
The angular distribution of mass by Bergman functions.
Let D = {z: |z| < 1} be the unit disk in the complex plane and denote by dA two-dimensional Lebesgue measure on D. For ε > 0 we define Σε = {z: |arg z| < ε}. We prove that for every ε > 0 there exists a δ > 0 such that if f is analytic, univalent and area-integrable on D, and f(0) = 0 thenThis problem arose in connection with a characterization by Hamilton, Reich and Strebel of extremal dilatation for quasiconformal homeomorphisms of D.
The angular distribution of mass by weighted Bergman functions.
The basic properties of Bloch functions.
The Bergman projection on weighted spaces: L¹ and Herz spaces
We find necessary and sufficient conditions on radial weights w on the unit disc so that the Bergman type projections of Forelli-Rudin are bounded on L¹(w) and in the Herz spaces .
The Bloch space for the minimal ball
We introduce the Bloch space for the minimal ball and we prove that this space can be identified with the dual of a certain analytic space which is strongly related to the Bergman theory on the minimal ball.
The C k Space
In this article, we formalize continuous differentiability of realvalued functions on n-dimensional real normed linear spaces. Next, we give a definition of the Ck space according to [23].
The Campanato, Morrey and Hölder spaces on spaces of homogeneous type
We investigate the relations between the Campanato, Morrey and Hölder spaces on spaces of homogeneous type and extend the results of Campanato, Mayers, and Macías and Segovia. The results are new even for the ℝⁿ case. Let (X,d,μ) be a space of homogeneous type and (X,δ,μ) its normalized space in the sense of Macías and Segovia. We also study the relations of these function spaces for (X,d,μ) and for (X,δ,μ). Using these relations, we can show that theorems for the Campanato, Morrey or Hölder spaces...
The canonical injection of the Hardy-Orlicz space into the Bergman-Orlicz space
We study the canonical injection from the Hardy-Orlicz space into the Bergman-Orlicz space .
The Cauchy transform of continuous linear functionals and projections on the weighted spaces of analytic functions.
The construction of normal bases for the space of continuous functions on , with the aid of operators
The essential norms of composition operators between generalized Bloch spaces in the polydisc and their applications.
The functor σ²X
We disprove the existence of a universal object in several classes of spaces including the class of weakly Lindelöf Banach spaces.
The Hölder duality for harmonic functions
The level function in rearrangement invariant spaces.
An exact expression for the down norm is given in terms of the level function on all rearrangement invariant spaces and a useful approximate expression is given for the down norm on all rearrangement invariant spaces whose upper Boyd index is not one.
The Lindelöf property and σ-fragmentability
In the previous paper, we, together with J. Orihuela, showed that a compact subset X of the product space is fragmented by the uniform metric if and only if X is Lindelöf with respect to the topology γ(D) of uniform convergence on countable subsets of D. In the present paper we generalize the previous result to the case where X is K-analytic. Stated more precisely, a K-analytic subspace X of is σ-fragmented by the uniform metric if and only if (X,γ(D)) is Lindelöf, and if this is the case then...
The logarithmic asymptotic expansions for the norms of evaluation functionals.
The martingale Smirnov class.
The multipliers of a space of almost convergent continuous functions
The Radon measures as functionals on Lipschitz functions