Lipschitz spaces of holomorphic and pluriharmonic functions on bounded symmetric domains in (N>1)
Littlewood-Paley Type Inequalities for M-harmonic Functions
Littlewood-Paley-Stein theory on Cn and Weyl multipliers.
Monge-Ampère measures and Poletsky-Stessin Hardy spaces on bounded hyperconvex domains
Poletsky-Stessin Hardy (PS-Hardy) spaces are the natural generalizations of classical Hardy spaces of the unit disc to general bounded, hyperconvex domains. On a bounded hyperconvex domain Ω, the PS-Hardy space is generated by a continuous, negative, plurisubharmonic exhaustion function u of the domain. Poletsky and Stessin considered the general properties of these spaces and mainly concentrated on the spaces where the Monge-Ampère measure has compact support for the associated exhaustion...
Morera theorem for holomorphic Hp spaces in the Heisenberg group.
Non-attainable boundary values of H∞ functions.
Nonfactorization theorems for Hardy and Bergman spaces on bounded symmetric domains
Norm and Taylor coefficients estimates of holomorphic functions in balls
A classical result of Hardy and Littlewood states that if is in , 0 < p ≤ 2, of the unit disk of ℂ, then where is a positive constant depending only on p. In this paper, we provide an extension of this result to Hardy and weighted Bergman spaces in the unit ball of , and use this extension to study some related multiplier problems in .
On an Estimate of Axler and Shapiro.
On Decomposition Theorems for Hardy Spaces on Domains in ... and Applications.
On Hardy spaces in complex ellipsoids
This paper deals with atomic decomposition and factorization of functions in the holomorphic Hardy space . Such representation theorems have been proved for strictly pseudoconvex domains. The atomic decomposition has also been proved for convex domains of finite type. Here the Hardy space was defined with respect to the ordinary Euclidean surface measure on the boundary. But for domains of finite type, it is natural to define with respect to a certain measure that degenerates near Levi-flat points...
On Hardy spaces on worm domains
In this review article we present the problem of studying Hardy spaces and the related Szeg˝o projection on worm domains. We review the importance of the Diederich–Fornæss worm domain as a smooth bounded pseudoconvex domain whose Bergman projection does not preserve Sobolev spaces of sufficiently high order and we highlight which difficulties arise in studying the same problem for the Szeg˝o projection. Finally, we announce and discuss the results we have obtained so far in the setting of non-smooth...
On Hardy-Lipschitz spaces
On -harmonic space .
On highly nonintegrable functions and homogeneous polynomials
We construct a sequence of homogeneous polynomials on the unit ball in which are big at each point of the unit sphere . As an application we construct a holomorphic function on which is not integrable with any power on the intersection of with any complex subspace.
On linear extension for interpolating sequences
Let A be a uniform algebra on X and σ a probability measure on X. We define the Hardy spaces and the interpolating sequences S in the p-spectrum of σ. We prove, under some structural hypotheses on A and σ, that if S is a “dual bounded” Carleson sequence, then S is -interpolating with a linear extension operator for s < p, provided that either p = ∞ or p ≤ 2. In the case of the unit ball of ℂⁿ we find, for instance, that if S is dual bounded in then S is -interpolating with a linear...
On M-harmonic space Bsp
On some characterizations of Carleson type measure in the unit ball.
On the automorphisms of circular and Reinhardt domains in complex Banach spaces.
On the Behavior of Holomorphic Functions Near Maximum Modulus Sets.