# Interpolation spaces of generalized smoothness and their applications to elliptic equations

@inproceedings{Anop2021InterpolationSO, title={Interpolation spaces of generalized smoothness and their applications to elliptic equations}, author={Anna V. Anop and Aleksandr Murach}, year={2021} }

We introduce and investigate classes of normed or quasinormed distribution spaces of generalized smoothness that can be obtained by various interpolation methods applied to classical Sobolev, Nikolskii –Besov, and Triebel – Lizorkin spaces. An arbitrary positive function O-regularly varying at infinity serves as the order of regularity for the spaces introduced. They are broad generalizations of the above classical spaces and allow being well defined on smooth manifolds. We give applications of…

## References

SHOWING 1-10 OF 101 REFERENCES

The refined Sobolev scale, interpolation and elliptic problems

- Mathematics
- 2012

The paper gives a detailed survey of recent results on elliptic problems in Hilbert spaces of generalized smoothness. The latter are the isotropic Hormander spaces H := B2,μ, with μ(ξ) = 〈ξ〉φ(〈ξ〉)…

Theory of Sobolev Multipliers: With Applications to Differential and Integral Operators

- Mathematics
- 2008

The purpose of this book is to give a comprehensive exposition of the theory of pointwise multipliers acting in pairs of spaces of differentiable functions. The theory was essentially developed by…

Hörmander Spaces, Interpolation, and Elliptic Problems

- Mathematics
- 2014

The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hormander function spaces. This…

A discrete transform and decompositions of distribution spaces

- Mathematics
- 1990

Abstract We study a representation formula of the form ƒ = ∑ Q 〈ƒ, ϑ Q 〉ψ Q for a distribution ƒ on R n. This formula is obtained by discretizing and localizing a standard Littlewood-Paley…

Methods of Approximation Theory

- Mathematics
- 2005

This monograph can be regarded as a result of the activity of many mathematicians of the 20th century in the field of classical Fourier series and the theory of approximation of periodic functions,…

Embeddings of Besov spaces of logarithmic smoothness

- Mathematics
- 2014

This paper deals with Besov spaces of logarithmic smoothness B-p,T(0,b) formed by periodic functions. We study embeddings of B-p,T(0,b) into Lorentz-Zygmund spaces L-p,L-q(log L)(beta). Our…

Spaces of generalized smoothness in the critical case: Optimal embeddings, continuity envelopes and approximation numbers

- Computer Science, MathematicsJ. Approx. Theory
- 2014

We study necessary and sufficient conditions for embeddings of Besov spaces of generalized smoothness B p , q ? , N ( R n ) into generalized Holder spaces ? ∞ , r µ ( ? ) ( R n ) when s ? ( N ? - 1 )…

Local growth envelopes of spaces of generalized smoothness: the subcriticalcase

- Mathematics
- 2004

The concept of local growth envelope (ℰLGA, u) of the quasi-normed function space A is applied to the spaces of generalized smoothness B(s,ψ) pq (ℝn) and F(s,ψ)pq (ℝn) and it is shown that the…

пРИБлИжЕНИЕ ФУНкцИИ МНОгИх пЕРЕМЕННых МН ОгОЧлЕНАМИ И пОпЕРЕЧНИкИ НЕкОтО Рых ФУНкцИОНАльНых к лАссОВ

- Mathematics
- 1982

Estimates of best polynomial approximation are obtained for the classesH[Ω] on parallelepipeds inRm. If the spectrum of the approximating polynomial is contained in the dilations of the original…

On Besov spaces of logarithmic smoothness and Lipschitz spaces

- Mathematics
- 2015

Abstract We compare Besov spaces B p , q 0 , b with zero classical smoothness and logarithmic smoothness b defined by using the Fourier transform with the corresponding spaces B p , q 0 , b defined…