Now showing items 22-41 of 43

• #### 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 ...
• #### On pointwise and weighted estimates for commutators of Calderón-Zygmund operators ﻿

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 ﻿

(Colloquium Mathematicum, 2019-03-22)
• #### Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions ﻿

(SIAM Journal on Mathematical Analysis, 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 ...
• #### 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} ...