Related papers: Norm estimates in Grand Lebesgue Spaces for some o…
We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of $\mathbb{R}^{n}$ and characterize precisely those that are bounded from Lebesgue spaces $L^{p}_{\alpha}$ into…
We extend in this article the classical imbedding theorems for fractional Lebesgue-Sobolev's spaces into the so-called Grand Lebesgue spaces, with sharp constant evaluation.
We obtain the estimate of the Lebesgue measure of the spectrum for the direct integral of matrix-valued functions. These estimates are applicable for a wide class of discrete periodic operators. For example: these results give new and sharp…
In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases.…
We generalize in this short paper the classical Luzin's theorem about existence of integral on the measurable function and its multidimensional analogues on the many popular classes of rearrangement invariant (r.i.) spaces, namely, on the…
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, more inequalities between the operator norm and its numerical radius, for the class of normal operators, are established. Some of the obtained results are based on recent reverse results for the Schwarz inequality in Hilbert…
We obtain one variant of the extrapolation theorem of Rubio de Fracia for variable exponent Lebesgue spaces. As a consequence we obtain conditions guarantee boundedness of strongly singular integral operators, singular integral operators…
In this article we investigate the Fourier series and transforms for the functions defined on the [-pi, pi]^ d or on the R^d and belonging to the (Bilateral) Grand Lebesgue Spaces. As a particular case we obtain some results about Fourier's…
Let a vector-valued sublinear operator satisfy the size condition and be bounded on weighted Lebesgue spaces with variable exponent. Then we obtain its boundedness on weighted grand Herz-Morrey spaces with variable exponents. Next we…
We give in this short paper the exact value for norms of two operators of Hardy-Sobolev type acting between two weight Grand Lebesgue Space (GLS) based on the whole multidimensional Euclidean space.
We investigate the structure of norm-preserving and linear but not necessarily surjective operators on variable-exponent, discrete Lebesgue spaces. A certain class of isometries, novel to this work, are especially considered; this class…
We compute the essential norm of inclusion operators, composition operators and multipliers acting from a closed subspace of some $L^p$-space into a subspace of some $L^q$-space, with $p > q.$
In this paper we give different estimates between Lebesgue norms of quadratic time-frequency representations. We show that, in some cases, it is not possible to have such bounds in classical $L^p$ spaces, but the Lebesgue norm needs to be…
In this article we introduce and investigate a new class of rearrangement invariant (r.i.) Banach function spaces, so-called Composed Grand Lebesgue Spaces (CGLS), in particular, Integral Grand Lebesgue Spaces (IGLS), which are some…
In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces. We prove a kind of \textit{reduction lemma} which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey…
Broadly speaking, this paper is concerned with dual spaces of operator algebras. More precisely, we investigate the existence of what we call Lebesgue projections: central projections in the bidual of an operator algebra that detect the…
We introduce Riesz potentials for non-Lebesgue measurable functions by taking the integrals in the sense of Choquet with respect to Hausdorff content and prove boundedness results for these operators. Some earlier results are recovered or…
In this paper it is investigated how to find a matrix representation of operators on a Hilbert space with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs).…
In this article mixed norm estimates are obtained for some integral operators, from which those for the Hermite semigroup and the Bochner Riesz means associated with the Hermite expansions are deduced. Also, mixed norm estimates for the…