Browsing Harmonic Analysis by Title
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Sawyertype inequalities for Lorentz spaces
(202206)The HardyLittlewood maximal operator M satisfies the classical Sawyertype estimate ∥Mfv∥L1,∞(uv)≤Cu,v‖f‖L1(u),where u∈ A1 and uv∈ A∞. We prove a novel extension of this result to the general restricted weak type case. ... 
Scattering with criticallysingular and δshell potentials
(2019)The authors consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a measure supported on a compact Lipschitz ... 
Selfimproving PoincaréSobolev type functionals in product spaces
(2021)In this paper we give a geometric condition which ensures that (q, p)Poincar´eSobolev inequalities are implied from generalized (1, 1)Poincar´e inequalities related to L 1 norms in the context of product spaces. ... 
Sharp constants in inequalities admitting the Calderón transference principle
(2023)The aim of this note is twofold. First, we prove an abstract version of the Calderón transference principle for inequalities of admissible type in the general commutative multilinear and multiparameter setting. Such an ... 
Sharp estimates for Jacobi heat kernels in conic domains
(2023)We prove genuinely sharp estimates for the Jacobi heat kernels introduced in the context of the multidimensional cone $\mathbb V^{d+1}$and its surface $\mathbb V^{d+1}_0$. To do so, we combine the theory of Jacobi polynomials ... 
Sharp reverse Hölder inequality for Cp weights and applications
(2020)We prove an appropriate sharp quantitative reverse Hölder inequality for the $C_p$ class of weights fromwhich we obtain as a limiting case the sharp reverse Hölder inequality for the $A_\infty$ class of weights (Hytönen ... 
Sharp weighted estimates involving one supremum
(201707)In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen. We also extend the result to rough homogeneous singular ... 
Sparse and weighted estimates for generalized Hörmander operators and commutators
(2019)In this paper a pointwise sparse domination for generalized Ho ̈rmander and also for iterated commutators with those operators is provided generalizing the sparse domination result in [24]. Relying upon that sparse domination ... 
Sparse bounds for maximal rough singular integrals via the Fourier transform
(20190312)We prove a quantified sparse bound for the maximal truncations of convolutiontype singular integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination principle by CondeAlonso, Culiuc, ... 
Sparse domination theorem for multilinear singular integral operators with $L^{r}$Hörmander condition
(20170401)In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the socalled multilinear $L^{r}$Hörmander condition, then $T$ can be dominated by multilinear sparse operators. 
Three Observations on Commutators of Singular Integral Operators with BMO Functions
(20160701)Three observations on commutators of Singular Integral Operators with BMO functions are exposed, namely 1  The already known subgaussian local decay for the commutator, namely $\[\frac{1}{Q}\left\left\{x\in Q\, : ... 
Topics in Harmonic Analysis; commutators and directional singular integrals
(20200301)This dissertation focuses on two main topics: commutators and maximal directional operators. Our first topic will also distinguish between two cases: commutators of singular integral operators and BMO functions and ... 
Twoweight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions
(2018)We investigate a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of ... 
Uniform maximal Fourier restriction for convex curves
(2024)We extend the estimates for maximal Fourier restriction operators proved by M\"{u}ller, Ricci, and Wright in \cite{MR3960255} and Ramos in \cite{MR4055940} to the case of arbitrary convex curves in the plane, with constants ... 
Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane
(201812)For electric and magnetic potentials with compact support, we consider the magnetic Schrödinger equation with fixed positive energy. Under a mild additional regularity hypothesis, and with fixed magnetic potential, we show ... 
Variation bounds for spherical averages
(20210622)We consider variation operators for the family of spherical means, with special emphasis on $L^p\to L^q$ estimates 
Vectorvalued extensions for fractional integrals of Laguerre expansions
(2018)We prove some vectorvalued inequalities for fractional integrals defined for several orthonormal systems of Laguerre functions. On the one hand, we obtain weighted $L^pL^q$ vectorvalued extensions, in a multidimensional ... 
Vectorvalued operators, optimal weighted estimates and the $C_p$ condition
(201809)In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ... 
Walter Rudin meets Elias M. Stein
(2023)Walter Rudin and Elias M. Stein were giants in the world of mathemat ics. They were loved and admired from students and researchers to teachers and academics, both young and old. They touched many of us through ... 
Weak and strong $A_p$$A_\infty$ estimates for square functions and related operators
(201707)We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound $[w]_{A_p} ...