A. A. Abdelhakim

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20152020

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math.AP2018

On the boundary terms in Hardy's inequalities for $W^{1, p}$ functions

Ahmed A. Abdelhakim

With the help of a radially invariant vector field, we derive inequalities of the Hardy kind, with no boundary terms, for $W^{1, p}$ functions on bounded star domains. Our results a…

math.AP2017

Limiting case Hardy inequalities on the sphere

Ahmed A. Abdelhakim

We give sharp limiting case Hardy inequalities on the sphere $S^{2}$ and show that their optimal constants are unattainable by any $f\in H^{1}\left(\mathbb{S}^{2}\right)\s…

math.AP2015

$L^{p}$ - $L^{q}$ boundedness of integral operators with oscillatory kernels: Linear versus quadratic phases

Ahmed A. Abdelhakim

Let $T_{N}^{j, k} : L^{p} (B) \to L^{q} ([0, 1])$ be the oscillatory integral operators defined by $\;\displaystyle T^{j,k}_{N}f(s):=\int_{B} \,f(x)\,e^{\imath N{|x|}^{j}s…

On the boundary terms in Hardy's inequalities for W1,p functions

Limiting case Hardy inequalities on the sphere

Lp-Lq boundedness of integral operators with oscillatory kernels: Linear versus quadratic phases

On the boundary terms in Hardy's inequalities for $W^{1, p}$ functions

$L^{p}$ - $L^{q}$ boundedness of integral operators with oscillatory kernels: Linear versus quadratic phases