Browsing Harmonic Analysis by Title
Now showing items 58-63 of 63
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Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane
(2018-12)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 ... -
Vector-valued extensions for fractional integrals of Laguerre expansions
(Studia Math., 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 ... -
Vector-valued operators, optimal weighted estimates and the $C_p$ condition
(Science China Mathematics, 2018-09)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 ... -
Weak and strong $A_p$-$A_\infty$ estimates for square functions and related operators
(Proceedings of the American Mathematical Society, 2017-07)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} ... -
Weighted mixed weak-type inequalities for multilinear operators
(Studia Mathematica, 2017)In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main ... -
Weighted norm inequalities for rough singular integral operators
(Journal of Geometric Analysis, 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 ...