Extending functions from Nikolskii-Besov spaces of mixed smoothness beyond a cube
Abstract
The article examines Nikolskii and Besov spaces with norms defined using "Lp-averaged" mixed moduli of continuity of functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative functions. The author builds continuous linear mappings of such spaces of functions defined on cube Id, to ordinary Nikolskii and Besov spaces of mixed smoothness in Rd, that are function extension operators, thus incurring coincidence of both kinds of spaces on the cube Id.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.