Pakistan Research Repository

Limiting Reiteration For Real Interpolation And Optimal Sobolev Embeddings

Ahmed, Irshaad (2011) Limiting Reiteration For Real Interpolation And Optimal Sobolev Embeddings. PhD thesis, Govt. College University, Lahore .



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.

Item Type:Thesis (PhD)
Uncontrolled Keywords:Mapping, Real, Theorems, Limiting, Embeddings, Rearrangement, Sobolev, Derivatives, Interpolation, Reiteration
Subjects:Physical Sciences (f) > Mathematics(f5)
ID Code:7275
Deposited By:Mr. Javed Memon
Deposited On:27 Dec 2011 09:00
Last Modified:27 Dec 2011 09:00

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