Oleg Vladimirovich Besov

Equivalent Norms in Spaces of Functions of Fractional Smoothness on Arbitrary Domains

AbstractIn this paper, we study the spaces Bpqs(G) and Lpqs(G) of functions f with positive exponent of smoothness s > 0 given on a domain

Embedding of Sobolev space in the case of the limit exponent

\user1{G} \subset \mathbb{R}^\user1{n}

Erratum to: “Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains in Lebesgue Spaces”

. The norms on these spaces are defined via integral norms of the difference of the function f of order m > s treated as a function of the point of the domain and of the difference increment. For an arbitrary domain

Extension by zero of functions of several variables

\user1{G} \subset \mathbb{R}^\user1{n}

Sobolev's embedding theorem for a domain with irregular boundary

, we characterize these spaces in terms of the local approximations of the function by polynomials of degree m − 1.

Эквивалентные нормы в пространствах функций дробной гладкости на произвольной области@@@Equivalent Norms in Spaces of Functions of Fractional Smoothness on Arbitrary Domains

We establish the embedding of the Sobolev space Wps(G) ⊂ Lq(G) for an irregular domain G in the case of a limit exponent under new relations between the parameters depending on the geometric properties of the domain G.