A. A. Abdelhakim

activity

20152020

collaborators

7 papers

math.FA2020

Optimal critical exponent $L^{p}$ inequalities of Hardy type on the sphere via Xiao's method

Ahmed A. Abdelhakim

First, we correct the proof presented in [Abimbola Abolarinwa, Kamilu Rauf, Songting Yin, Sharp $L^{p}$ Hardy type and uncertainty principle inequalities on the sphere, Journal of…

math.FA2020

Sharp subcritical and critical $L^{p}$ Hardy inequalities on the sphere

Ahmed A. Abdelhakim

We prove sharp inequalities of Hardy type for functions in the Sobolev space $W^{1, p}$ on the unit sphere $S^{n - 1}$ in $R^{n}$ . We achieve this in both the subcri…

math.CA2018

Precise interpretation of the conformable fractional derivative

Ahmed A. Abdelhakim

Let $α \in] 0, 1 [$ . We prove that the existence of the conformable fractional derivative $T_{α} f$ of a function $f : [0, \infty [⟶ R$ introduced by Khalil et al.…

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…

Optimal critical exponent Lp inequalities of Hardy type on the sphere via Xiao's method

Sharp subcritical and critical Lp Hardy inequalities on the sphere

Precise interpretation of the conformable fractional derivative

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

Optimal critical exponent $L^{p}$ inequalities of Hardy type on the sphere via Xiao's method

Sharp subcritical and critical $L^{p}$ Hardy inequalities on the sphere

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