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Infinitesimal Carleson property for weighted measures induced by analytic self-maps of the unit disk
Calderón-Zygmund decomposition Carleson measure weighted Bergman space
2012/6/21
We prove that, for every $\alpha > -1$, the pull-back measure $\phi ({\cal A}_\alpha)$ of the measure $d{\cal A}_\alpha (z) = (\alpha + 1) (1 - |z|^2)^\alpha \, d{\cal A} (z)$, where ${\cal A}$ is the...
Real analytic expansion of spectral projection and extension of Hecke-Bochner identity
Coxeter group Hecke-Bochner identity Heisenberg group Laguerre polynomials spherical harmonics twisted convolution
2012/4/16
In this article, we review the Weyl correspondence of bigraded spherical harmonics and use it to extend the Hecke-Bochner identities for the spectral projections $f\times\varphi_k^{n-1}$ for function ...
Real analytic approximations which almost preserve Lipschitz constants of functions defined on the Hilbert space
Real analytic approximations Lipschitz constants of functions defined Hilbert space
2011/2/24
Let X be a separable real Hilbert space. We show that for every Lipschitz function f : X ! R, and for every " > 0, there exists a Lipschitz, real analytic function g : X ! R such that |f(x) − g(...
Boundary values in range spaces of co-analytic truncated Toeplitz operators
Continuation Model spaces Toeplitz operators Truncated Toeplitz operators
2011/2/22
Functions in backward shift invariant subspaces have nice analytic continuation properties outside the spectrum of the inner function defining the space. Inside the spectrum of the inner function.
On a Certain Subclass of Analytic Functions Involving the Al-Oboudi Differential Operator
Close-to-convex function Close-to-starlike function Ruscheweyh derivative operator Al-Oboudi differential operator and subordination relationship
2010/1/22
In this paper we introduce a new subclass of normalized analytic functions in the open unit disc which is defined by the Al-Oboudi differential operator. A coefficient inequality, extreme points and i...