Research papers

On the compactness principle in variable space $L^p$ for periodic composite structures

V. V. Shumilova

Branch of the Moscow Psychology-Social Institute, Murom

Abstract: We consider the compactness principle in the variable space $L^p$ related to a periodic Borel measure. It is supposed that the periodic Borel measure describes a periodic singular or composite structure. We prove the compactness principle for periodic grids, box structures, involving Cantor's constructions, and corresponding composite structures.

Keywords: periodic structures, periodic Borel measure, compactness principle.

UDC: 517.98

MSC: 46B50

Received April 28, 2008, published December 23, 2009

Bibliographic databases:

• 
•