Add to ORKGLet e be a homogeneous subset of R in the sense of Carleson. Let μ be a finite positive measure on R and H_μ(x) its Hilbert transform. We prove that if lim_(t→∞)t|e∩{x||H_μ(x)|>t}| = 0, then μ_s(e) = 0, where μ_s is the singular part of μ
We extend some remarkable recent results of Lubinsky and Levin–Lubinsky from [−1, 1] to allow discre...
The 2D Euler equations with random initial condition distributed as a certain Gaussian measure are c...
AbstractThe best approximation of functions in Lp(Sd−1),0<p<1 by spherical harmonic polynomials is s...
AbstractThe Lp norm of the Hilbert transform of the characteristic function of a set is invariant wi...
Let $\mu$ be a positive Borel measure on the interval [0,1). For $\alpha>0$, the Hankel matrix $\mat...
Abstract In 1923 A. Khinchin asked if given any B ⊆ [0, 1) of positive Lebesgue measure, we have ...
This paper is concerned with the boundary behavior of solutions of the Helmholtz equation in $\mathb...
AbstractBy introducing two pairs of conjugate exponents and estimating the weight coefficients, we g...
We consider, for a class of functions $\varphi : \mathbb{R}^{2} \setminus \{ {\bf 0} \} \to \mathbb{...
AbstractIn this note we develop a notion of integration with respect to a bimeasure μ that allows in...
In this paper we study the Hausdorff dimension of a elliptic measure μf in space associated to a pos...
For a finite positive Borel measure $\mu$ on $(0,1)$ we consider an infinite matrix $\Gamma_\mu$ whi...
AbstractWe give an alternative proof of a theorem of Stein and Weiss: The distribution function of t...
For a finite positive Borel measure $\mu$ on $(0,1)$ we consider an infinite matrix $\Gamma_\mu$ whi...
We prove that, for every α>−1, the pull-back measure φ(Aα) of the measure dAα(z)=(α+1)(1−|z|2)αdA(...
We extend some remarkable recent results of Lubinsky and Levin–Lubinsky from [−1, 1] to allow discre...
The 2D Euler equations with random initial condition distributed as a certain Gaussian measure are c...
AbstractThe best approximation of functions in Lp(Sd−1),0<p<1 by spherical harmonic polynomials is s...
AbstractThe Lp norm of the Hilbert transform of the characteristic function of a set is invariant wi...
Let $\mu$ be a positive Borel measure on the interval [0,1). For $\alpha>0$, the Hankel matrix $\mat...
Abstract In 1923 A. Khinchin asked if given any B ⊆ [0, 1) of positive Lebesgue measure, we have ...
This paper is concerned with the boundary behavior of solutions of the Helmholtz equation in $\mathb...
AbstractBy introducing two pairs of conjugate exponents and estimating the weight coefficients, we g...
We consider, for a class of functions $\varphi : \mathbb{R}^{2} \setminus \{ {\bf 0} \} \to \mathbb{...
AbstractIn this note we develop a notion of integration with respect to a bimeasure μ that allows in...
In this paper we study the Hausdorff dimension of a elliptic measure μf in space associated to a pos...
For a finite positive Borel measure $\mu$ on $(0,1)$ we consider an infinite matrix $\Gamma_\mu$ whi...
AbstractWe give an alternative proof of a theorem of Stein and Weiss: The distribution function of t...
For a finite positive Borel measure $\mu$ on $(0,1)$ we consider an infinite matrix $\Gamma_\mu$ whi...
We prove that, for every α>−1, the pull-back measure φ(Aα) of the measure dAα(z)=(α+1)(1−|z|2)αdA(...
We extend some remarkable recent results of Lubinsky and Levin–Lubinsky from [−1, 1] to allow discre...
The 2D Euler equations with random initial condition distributed as a certain Gaussian measure are c...
AbstractThe best approximation of functions in Lp(Sd−1),0<p<1 by spherical harmonic polynomials is s...