Related papers: Exact norm estimates for multivariate dilation ope…
The paper is devoted to the problem of exact calculation of the norms in ideal spaces for monotone operators on the cones of functions with monotonicity properties. We implement a general approach to this problem that covers many concrete…
We prove $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups; these are sharp up to two endpoints. The results can be applied to improve currently known bounds on sparse…
The operator-valued multiplier theorems in weighted abstract Besov spaces are studied. These results permit us to show embedding theorems in weighted Besov-Lions type spaces. The most regular class of interpolation space is found such that…
Variable Muckenhoupt weights are considered in variable exponent Lebesgue spaces. Applications are given for polynomial approximation in these spaces. Boundedness of averaging operator is proved to gain a transference result. Almost all…
We develop a theory of extrapolation for weights that satisfy a generalized reverse H\"older inequality in the scale of Orlicz spaces. This extends previous results by Auscher and Martell [2] on limited range extrapolation. As an…
We characterize the dual spaces of the generalized Hardy spaces defined by replacing Lebesgue quasi-norms by Wiener amalgam ones. In these generalized Hardy spaces, we prove that some classical linear operators such as Calder\'on-Zygmund,…
In this work it is described all normal extensions of a multipoint minimal operator generated by linear multipoint differential-operator expression for second order in the Hilbert space of vector-functions in terms of boundary values at the…
We study two classes of bounded operators on mixed norm Lebesgue spaces, namely composition operators and product operators. A complete description of bounded composition operators on mixed norm Lebesgue spaces are given. For a certain…
In this note we present the metric approximation property for weighted mixed-norm $L_w^{(p_1,\dots ,p_n)}$ and variable exponent Lebesgue type spaces. As a consequence, this also implies the same property for modulation and Wiener-Amalgam…
In this paper we obtain the non - asymptotic estimations of Poincare type between function and its gradient in the so - called Bilateral Grand Lebesgue Spaces. We also give some examples to show the sharpness of these inequalities.
In this work we obtain boundedness on weighted variable Lebesgue spaces of some maximal functions that come from the localized analysis considering a critical radius function. This analysis appears naturally in the context of the…
We give two weighted norm estimates for higher order commutator of classical operators such as singular integral and fractional type operators, between weighted $L^p$ and certain spaces that include Lipschitz, BMO and Morrey spaces. We also…
We will give an outline of the main results in our recent AMS Memoir, and include some new results, exposition and open problems. In that memoir we developed a general dilation theory for operator valued measures acting on Banach spaces…
We establish weighted extrapolation theorems in classical and grand Lorentz spaces. As a consequence we have the weighted boundedness of operators of Harmonic Analysis in grand Lorentz spaces. We treat both cases: diagonal and off-diagonal…
In this paper, we investigate operators on Riesz algebras, which are continuous with respect to multiplicative modifications of order convergence and relatively uniform convergence. We also introduce and study mo-Lebesgue, mo-$KB$, and…
In this paper we prove weighted mixed norm estimates for Riesz transforms associated to Hermite and special Hermite operators. The estimates are shown to be equivalent to vectorvalued esimates for a sequence of operators defined in terms of…
We obtain in this short article the bilateral non-asymptotic estimations for the norm in Lebesgue-Riesz and bilateral Grand Lebesgue spaces of the so-called fractional Laplace integral transform. We give also examples to show the sharpness…
We prove the sharp regularizing estimates for the gain term of the Boltzmann collision operator including hard sphere, hard potential and Maxwell molecule models. Our new estimates characterize both regularization and convolution properties…
This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a…
We study in this short report the boundedness of classical non-linear operators: Nemytskii, Urysohn, Hammerstein acting from one Grand Lebesgue Space to another one, and deduce some its upper norm estimates. We bring also some examples to…