A. A. Abdelhakim

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20152020

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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.FA2015

On the summablility of truncated double Fourier series

Ahmed A. Abdelhakim

We estimate the truncated double trigonometric series $\sum_{n = 0}^{N} \sum_{m = 0}^{M} a_{mn} e^{2 π  (m x + n y)}$ , $a_{mn} \in C$ , in Lebesgue spaces with mixe…

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

On the summablility of truncated double Fourier series

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