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Title of Thesis

Limiting Reiteration For Real Interpolation And Optimal Sobolev Embeddings

Author(s)

Irshaad Ahmed

Institute/University/Department Details
Abdus Salam School of Mathematical Sciences / GC University, Lahore
Session
2011
Subject
Mathematics
Number of Pages
118
Keywords (Extracted from title, table of contents and abstract of thesis)
Mapping, Real, Theorems, Limiting, Embeddings, Rearrangement, Sobolev, Derivatives, Interpolation, Reiteration

Abstract
Firstly, sharp reiteration theorems for the K􀀀interpolation method in limiting cases are proved using two-sided estimates of the K􀀀functional. As an application, sharp mapping properties of the Riesz potential are derived in a limiting case. Secondly, we prove optimal embeddings of the homogeneous Sobolev spaces built-up over function spaces in Rn with K􀀀monotone and rearrangement invariant norm into another rearrangement invariant function spaces. The investigation is based on pointwise and integral estimates of the rearrangement or the oscillation of the rearrangement of f in terms of the rearrangement of the derivatives of f.

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S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

 
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2

1

REITERATION FOR THE K..INTERPOLATION METHOD IN LIMITING CASES


1.1 Introduction
1.2 Estimates of the K􀀀functional
1.3 Auxiliary results and embeddings
1.4 Reiteration theorems
1.5 An application

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3 2 OPTIMAL EMBEDDINGS OF GENERALIZED HOMOGENEOUS SOBOLEV SPACES 5

2.1 Introduction
2.2 Pointwise estimates involving the decreasing rearrangements
2.3 The generalized homogeneous Sobolev spaces
2.4 Admissible couples
2.5 Optimal norms

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4 3 BIBLIOGRAPHY

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