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Now showing items 1-10 of 15

#### A Decomposition of Calderón–Zygmund Type and Some Observations on Differentiation of Integrals on the Infinite-Dimensional Torus

(2020-02-13)

In this note we will show a Calder\'on--Zygmund decomposition associated with a function $f\in L^1(\mathbb{T}^{\omega})$. The idea relies on an adaptation of a more general result by J. L. Rubio de Francia in the setting ...

#### Maximal estimates for a generalized spherical mean Radon transform acting on radial functions

(2020)

We study a generalized spherical means operator,
viz.\ generalized spherical mean Radon transform, acting on radial functions.
As the main results, we find conditions for the associated maximal operator and its local ...

#### Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function

(2019-12)

We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping.
Quantitative weighted estimates are obtained for this operator. ...

#### On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians

(2019-09)

We obtain generalised trace Hardy inequalities for fractional powers of general operators given by sums of squares of vector fields. Such inequalities are derived by means of particular solutions of an extended equation ...

#### On the absolute divergence of Fourier series in the infinite dimensional torus

(2019-03-22)

In this note we present some simple counterexamples, based on quadratic forms in infinitely many variables, showing that the implication
$f\in C^{(\infty}(\mathbb{T}^\omega)\Longrightarrow\sum_{\bar{p}\in\mathbb{Z}^\inf ...

#### $A_1$ theory of weights for rough homogeneous singular integrals and commutators

(2019)

Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $\BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved:
\[
\|T_\Omega ...

#### Weighted norm inequalities for rough singular integral operators

(2018-08-17)

In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner--Riesz multiplier at the critical index ...

#### Hardy-type inequalities for fractional powers of the Dunkl-Hermite operator

(2018)

We prove Hardy-type inequalities for a fractional Dunkl–Hermite operator, which incidentally gives Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use h-harmonic expansions to reduce the ...

#### Vector-valued extensions for fractional integrals of Laguerre expansions

(2018)

We prove some vector-valued inequalities for fractional integrals defined for several orthonormal systems of Laguerre functions. On the one hand, we obtain weighted $L^p-L^q$ vector-valued extensions, in a multidimensional ...

#### Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications

(2018)

The analysis of nonlocal discrete equations driven by
fractional powers of the discrete Laplacian on a mesh of size $h>0$
\[
(-\Delta_h)^su=f,
\]
for $u,f:\Z_h\to\R$, $0<s<1$, is performed. The pointwise nonlocal ...