THE BOUNDEDNESS OF BAND-LIMITEDWAVELET DECOMPOSITION OPERATOR IN MORREY SPACE

• Main Author: Alif Aqsha, Muhammad
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/54999
• Institution: Institut Teknologi Bandung

The study of function spaces such as Lebesgue and Morrey spaces is motivated by the need to solve partial differential equations that are apparent in many problems such as physical phenomena. To examine such functions, a decomposition which breaks down those functions into several simpler functions is needed. One of those simpler functions are wavelets. Wavelets are functions descended from a single mother function which is modified only by translation and dilation. This research primarily concerns wavelets which are orthonormal and band-limited. One method to decompose Lebesgue and Morrey functions is through the use of a waveletrelated operator called the W! operator, where the ! is the mother function. In this study, we described a norm equivalency between Lebesgue functions and their mapped functions through the W! operator. Afterwards, we tried to extend this result into Morrey spaces and obtained the boundedness of this operator or a halfequivalency.