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Limiting Reiteration for Real Interpolation and Optimal Sobolev Embeddings

Thesis Info

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Author

Irshaad Ahmed

Supervisor

Georgi Eremiev Karadzhov

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2006

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/2037

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726583618

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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 R n 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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