Now showing items 23-42 of 59

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

(Annali de Matematica Pura et Applicata, 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 ...
• #### Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions ﻿

(Transactions of the American Mathematical Society, 2017)
Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the Dunkl--Hermite operator ...
• #### Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer ﻿

(Colloquium Mathematicum, 2016-01-01)
In this paper we study mixed weighted weak-type inequal- ities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from [CMP2].
• #### Multilinear singular integrals on non-commutative lp spaces ﻿

(Springer International Publishing, 2019)
We prove Lp bounds for the extensions of standard multilinear Calderón- Zygmund operators to tuples of UMD spaces tied by a natural product structure. The product can, for instance, mean the pointwise product in UMD ...
• #### New bounds for bilinear Calderón-Zygmund operators and applications ﻿

(Revista Matemática Iberoamericana, 2016-11-25)
In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following ...
• #### Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications ﻿

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 ...
• #### A note on generalized Poincaré-type inequalities with applications to weighted improved Poincaré-type inequalities ﻿

(2020)
The main result of this paper supports a conjecture by C. P\'erez and E. Rela about the properties of the weight appearing in their recent self-improving result of generalized inequalities of Poincar\'e-type in the Euclidean ...
• #### A note on the off-diagonal Muckenhoupt-Wheeden conjecture ﻿

(WSPC Proceedings, 2016-07-01)
We obtain the off-diagonal Muckenhoupt-Wheeden conjecture for Calderón-Zygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the Hardy-Littlewood maximal function satisfies the following ...
• #### The observational limit of wave packets with noisy measurements ﻿

(2019)
The authors consider the problem of recovering an observable from certain measurements containing random errors. The observable is given by a pseudodifferential operator while the random errors are generated by a Gaussian ...
• #### On Bloom type estimates for iterated commutators of fractional integrals ﻿

(Indiana University Mathematics Journal, 2018-04)
In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from [15]. We give new proofs for those inequalities relying upon a new sparse ...
• #### On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians ﻿

(Communications on pure and applied analysis, 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 ...