Related papers: Young type inequalities for weighted spaces
We state and verify up to weight 172 a conjecture on the existence of a certain generating set for spaces of classical Siegel modular forms. This conjecture is particularly useful for calculations involving Fourier expansions. Using this…
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…
In this paper a reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator $T$ with the Hardy and Copson operators in weighted Lebesgue spaces are proved. New equivalence theorems are obtained for…
In this work we obtain boundedness results for fractional operators associated with Schr\"odinger operators $\ \mathcal{L}=-\Delta+V$ on weighted variable Lebesgue spaces. These operators include fractional integrals and their respective…
This work explores new deep connections between John-Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of $BMO$-type spaces. The results are formulated in a very general framework in which $BMO$ spaces are…
Leibniz-type rules for Coifman-Meyer multiplier operators are studied in the settings of Triebel-Lizorkin and Besov spaces associated to weights in the Muckenhoupt classes. Even in the unweighted case, improvements on the currently known…
In the article, some Huygens and Wilker type inequalities involving trigonometric and hyperbolic functions are refined and sharpened.
With the help of Van der Corput lemmas, decay estimates are proven for Fourier transforms of mixed homogeneous hypersurface measures with densities that can be quite irregular. The primary results are local in nature, but can be extended to…
We investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of fractional parabolic and elliptic equations.
In this paper we show that the Fourier transform induces an isomorphism between the coorbit spaces defined by Feichtinger and Gr\"ochenig of the mixed, weighted Lebesgue spaces $L_{v}^{p,q}$ with respect to the quasi-regular representation…
In this paper, new sharpened Huygens type inequalities involving Bessel and modified Bessel functions of the first kinds are established
To study statistical properties of modular forms, including for instance Sato-Tate like problems, it is essential to have a large number of Fourier coefficients. In this article, we exhibit three bases for the space of modular forms of any…
In this article we study some new pointwise inequalities between rough singular integral operators, weighted maximal functions of the gradient and weighted Morrey spaces. These pointwise estimates will naturally lead us to a new class of…
In this short article we obtain the non-asymptotic upper and low estimations for linear and bilinear weight Riesz's functional through the Lebesgue spaces.
Given a matrix-weight $W$ in the Muckenhoupt class $\mathbf{A}_p(\mathbb{R}^n)$, $1\leq p<\infty$, we introduce corresponding vector-valued continuous and discrete $\alpha$-modulation spaces $M^{s,\alpha}_{p,q}(W)$ and…
We obtain necessary and sufficient conditions on weights for the generalized Fourier-type transforms to be bounded between weighted $L^p-L^q$ spaces. As an important example, we investigate transforms with kernel of power type, as for…
We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to L\^e and Teissier, which reformulates Whitney regularity in terms of conormal…
We prove that for every radial weighted Fock space, the system biorthogonal to a complete and minimal system of reproducing kernels is also complete under very mild regularity assumptions on the weight. This result generalizes a theorem by…
We obtain three types of results in this paper. Firstly we improve Leray's inequality by providing several types of reminder terms, secondly we introduce several Hilbert spaces based on these improved Leray inequalities and discuss their…
We introduce the Hardy spaces for Fourier integral operators on Riemannian manifolds with bounded geometry. We then use these spaces to obtain improved local smoothing estimates for Fourier integral operators satisfying the cinematic…