The structure of fractional spaces generated by multi-dimensional elliptic difference operator

Non-elliptic Structure of the Ricci Operator

Rjk = R̄jk + ∇̄mD jk − ∇̄jD mk −Dn jkD nm −Dn mkD nj . (To see why this is true, just compute in local normal coordinates for ḡ!) From now on all components are tensorial (as opposed to local coordinate components.) The terms involving second covariant derivatives of the metric are: 1 2 g(−∇̄m∇̄lgjk +∇̄m∇̄kgjl +∇̄m∇̄jglk +∇̄j∇̄lgmk−∇̄j∇̄kgml−∇̄j∇̄mglk). The first term is a kind of Laplacian. The third and six...

Weighted estimates of higher order commutators generated by BMO-functions and the fractional integral operator on Morrey spaces

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

Fractional Integration Operator of Variable Order in the Holder Spaces

The fractional integrals I+(x)0 of variable order e(x) are considered. A theorem on mapping properties of Ia+ in Holder-type spaces H is proved, this being a generalization of the well known Hardy-Li ttlewood theorem. KEYWORDSFractional integration, variable fractional order, mapping properties, Holder continuous functions, Hardy-Littlewood theorem. 1991 AHS SUBJECT CLASSIFICATION CODES. 26 A33...

A Comparison Result for the Fractional Difference Operator

In this paper, we deduce the Green’s function for a ν-th order, 1 < ν ≤ 2, discrete fractional boundary value problem with boundary conditions of the type αy(ν−2)−β∆y(ν−2) = 0, γy(ν+ b)+δ∆y(ν+ b) = 0, for α, β, γ, δ ≥ 0 and αγ+αδ+βγ 6= 0. This extends and generalizes the results of some recent papers. We then show that this Green’s function satisfies a positivity property. From this we deduce a...