NORM ESTIMATES OF FRACTIONAL INTEGRAL OPERATORS BY RIESZ TRANSFORM IN WEIGHTED LEBESGUE SPACES

NORM ESTIMATES OF FRACTIONAL INTEGRAL OPERATORS BY RIESZ TRANSFORM IN WEIGHTED LEBESGUE SPACES

In this thesis we discuss behaviour of fractional integral operators on weighted Lebesgue spaces of exponent 1. First we give a counterexample for the boundedness result of fractional integral operators in weighted Lebesgue spaces of exponent 1. We also prove a norm estimate of fractional integra...

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Bibliographic Details
Main Author: Dita Kumala, Mei
Format: Theses
Language:Indonesia
Online Access:https://digilib.itb.ac.id/gdl/view/79577
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Institution: Institut Teknologi Bandung
Language: Indonesia
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Summary:In this thesis we discuss behaviour of fractional integral operators on weighted Lebesgue spaces of exponent 1. First we give a counterexample for the boundedness result of fractional integral operators in weighted Lebesgue spaces of exponent 1. We also prove a norm estimate of fractional integral operators by Riesz transform in weighted Lebesgue spaces of exponent 1. As an application, we also establish a similar result for fractional maximal operators and an end-point case of Olsen’s inequalities in weighted Lebesgue spaces.

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