Related papers: Interpolation schemes in weighted Bergman spaces
The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given.
In this paper we obtain some weighted generalizations of Ostrowski type inequalities on time scales involving combination of weighted {\Delta}-integral means, i.e., a weighted Ostrowski type inequality on time scales involving combination…
A treatment of (generalized) Clemens-Schmid exact sequences from the perspective of weights.
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…
Interpolation inequalities in Triebel-Lizorkin-Lorentz spaces and Besov-Lorentz spaces are studied for both inhomogeneous and homogeneous cases. First we establish interpolation inequalities under quite general assumptions on the parameters…
The Hermite interpolation formulas are based on the interpretation of interpolation nodes as roots of suitable polynomials. Therefore, such formulas belong to the class of algebraic interpolations. The article considers a multidimensional…
Interpolated multiple $q$-zeta values are deformation of multiple $q$-zeta values with one parameter, $t$, and restore classical multiple zeta values as $t = 0$ and $q \to 1$. In this paper, we discuss generating functions for sum of…
If $\fA$ is a unital weak-$*$ closed algebra of multiplication operators on a reproducing kernel Hilbert space which has the property $\bA_1(1)$, then the cyclic invariant subspaces index a Nevanlinna-Pick family of kernels. This yields an…
We propose an explicit construction of a weighted generalised Grassmannian. For a weighted Grassmannian (i.e., for series A) we obtain an effective parametrisation of possible $\mathbb{Z}$-gradings on Pl\"{u}cker coordinates, and provide…
In a previous work, "compact versions" of Rubio de Francia's weighted extrapolation theorem were proved, which allow one to extrapolate the compactness of an linear operator from just one space to the full range of weighted Lebesgue spaces,…
We characterize strong continuity of general operator semigroups on some Lebesgue spaces. In particular, a characterization of strong continuity of weighted composition semigroups on classical Hardy spaces and weighted Bergman spaces with…
We show that Rochberg's generalizared interpolation spaces $\mathscr Z^{(n)}$ arising from analytic families of Banach spaces form exact sequences $0\to \mathscr Z^{(n)} \to \mathscr Z^{(n+k)} \to \mathscr Z^{(k)} \to 0$. We study some…
In the theory of nonlinear partial differential equations we need to explain superposition operators. For modulation spaces equipped with particular ultradifferentiable weights this was done in \cite{rrs}. In this paper we introduce a class…
The interpolation of couples of separable Hilbert spaces with a function parameter is studied. The main properties of the classic interpolation are proved. Some applications to the interpolation of isotropic H\"ormander spaces over a closed…
Over an algebraically closed field, the $\textit{double point interpolation}$ problem asks for the vector space dimension of the projective hypersurfaces of degree $d$ singular at a given set of points. After being open for 90 years, a…
In this paper, we obtain two interpolation theorems on convex-set valued Lebesgue spaces, which generalize the Marcinkiewicz interpolation theorem and Riesz-Thorin interpolation theorem on classical Lebesgue spaces, respectively. As…
We obtain a characterization of complete interpolating sequences in a class of Fock-type spaces with radial weights for which such sequences exist. Our criterion is formulated in terms of logarithmic separation and controlled perturbations…
We are interested in the norm of the inclusion between the standard weighted Bergman spaces $A^2_\alpha$ and $A^p_{\frac{p}{2} (\alpha + 2)-2}$, $p > 2$, which is conjectured to be contractive by O.F. Brevig, J. Ortega-Cerd\`a, K. Seip and…
We construct the new q-extension of Bernoulli numbers and polynomials in this paper. Finally we consider the q-zeta functions which interpolate the new q-extension of Bernoulli numbers and polynomials.
We characterise the complex interpolation spaces of weighted vector-valued Sobolev spaces with and without boundary conditions on the half-space and on smooth bounded domains. The weights we consider are power weights that measure the…