Browsing Harmonic Analysis by Title
Now showing items 35-54 of 79
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Maximal estimates for a generalized spherical mean Radon transform acting on radial functions
Ciaurri Ó.; Nowak, A.; Roncal, L.
(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 ... -
Maximal operators on the infinite-dimensional torus
Roncal, Luz; Kosz, D.; Martínez-Perales, J.; Paternostro, V.; Rela, E.; Roncal, L. (2022-03-31)
We study maximal operators related to bases on the infinite-dimensional torus $\tom$. {For the normalized Haar measure $dx$ on $\mathbb{T}^\omega$ it is known that $M^{\mathcal{R}_0}$, the maximal operator associated with ... -
Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions
Boggarapu, P.; Roncal, L.; Thangavelu, S. (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
Ombrosi, S.; Pérez, C. (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 operator-valued calderón-zygmund theory
(2020)We develop a general theory of multilinear singular integrals with operator- valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the R-boundedness ... -
Multilinear singular integrals on non-commutative lp spaces
(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
(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
Ciaurri Ó.; Roncal, L.; Stinga, P.R.; Torrea, J.L.; Varona, J.L. (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 ... -
A note on generalized Fujii-Wilson conditions and BMO spaces
Ombrosi, S.; Pérez, C.; Rela, E.; Rivera-Ríos, I. (2020-07-01)
In this note we generalize the definition of the Fujii-Wilson condition providing quantitative characterizations of some interesting classes of weights, such as A∞, A∞weak and Cp, in terms of BMO type spaces suited to them. ... -
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
Cruz-Uribe, D.; Martell, J.M.; Pérez, C. (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
(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
Boggarapu, P.; Roncal, L.; Thangavelu, S. (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 pointwise and weighted estimates for commutators of Calderón-Zygmund operators
(2017)In recent years, it has been well understood that a Calderón-Zygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar ... -
On sums involving Fourier coefficients of Maass forms for SL(3,Z)
(2016-09-10)We derive a truncated Voronoi identity for rationally additively twisted sums of Fourier coefficients of Maass forms for SL(3,Z), and as an application obtain a pointwise estimate and a second moment estimate for the sums ... -
On the absolute divergence of Fourier series in the infinite dimensional torus
Fernández, E.; Roncal, L. (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 ... -
Pointwise Convergence over Fractals for Dispersive Equations with Homogeneous Symbol
Eceizabarrena, D.; Ponce Vanegas, F. (2021-08-24)
We study the problem of pointwise convergence for equations of the type $i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and non-singular. We prove that for initial data $f\in H^s(\mathbb{R}^n)$ ... -
Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates
Li, K.; Ombrosi, S.; Pérez, C. (2018-09)
We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that $$\Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, ... -
A quantitative approach to weighted Carleson condition
(2017-05-05)Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator \[ \mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0 \] are ...