Atomic decomposition of Besov spaces with variable smoothness and integrability
نویسندگان
چکیده
منابع مشابه
Function Spaces of Variable Smoothness and Integrability
A. In this article we introduce Triebel–Lizorkin spaces with variable smoothness and integrability. Our new scale covers spaces with variable exponent as well as spaces of variable smoothness that have been studied in recent years. Vector-valued maximal inequalities do not work in the generality which we pursue, and an alternate approach is thus developed. Applying it, we give molecular ...
متن کاملSharp Embeddings of Besov Spaces with Logarithmic Smoothness
We prove sharp embeddings of Besov spaces B p,r (R ) with the classical smoothness σ and a logarithmic smoothness α into Lorentz-Zygmund spaces. Our results extend those with α = 0, which have been proved by D. E. Edmunds and H. Triebel. On page 88 of their paper (Math. Nachr. 207 (1999), 79–92) they have written: “Nevertheless a direct proof, avoiding the machinery of function spaces, would be...
متن کاملDecomposition of Besov-Morrey Spaces
We establish a decomposition of Besov-Morrey spaces in terms of smooth “wavelets” obtained from a Littlewood-Paley partition of unity, or more generally molecules concentrated on dyadic cubes. We show that an expansion in atoms supported on dyadic cubes holds. We study atoms in Morrey spaces and prove a Littlewood-Paley theorem. Our results extend those of M. Frazier and B. Jawerth for Besov sp...
متن کاملApproximation and entropy numbers in Besov spaces of generalized smoothness
Let X and Y be Banach (or quasi-Banach) spaces and let T ∈ L(X,Y ) be a compact operator. In order to measure “the degree of compactness of T” one can use the asymptotic decay of the sequence of approximation numbers of T or the decay of the sequence of entropy numbers of T. In general, the behaviour of these sequences is quite different. However, as we shall show, under certain assumptions the...
متن کاملOn an atomic decomposition in Banach spaces
An atomic decomposition is considered in Banach space. A method for constructing an atomic decomposition of Banach space, starting with atomic decomposition of subspaces is presented. Some relations between them are established. The proposed method is used in the study of the frame properties of systems of eigenfunctions and associated functions of discontinuous differential operators.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2012
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2011.11.035