arXiv subjects

I. Abu-Falahah

Publications and source records attributed to I. Abu-Falahah.

2 recordsLinked to original sources

arXiv2013

A note on the almost everywhere convergence to initial data for some evolution equations

The weighted Lebesgue spaces of initial data for which almost everywhere convergence of the heat equation holds was only very recently characterized. In this note we show that the same weighted space of initial data is optimal for the heat--diffusion parabolic equations involving the harmonic oscillator and the Ornstein--Uhlenbeck operator.

math.AP↗

arXiv2011

Square functions associated to Schrodinger operators

We characterize geometric properties of Banach spaces in terms of boundedness of square functions associated to general Schrodinger operators of the form $L=-Δ+V$, where the nonnegative potential $V$ satisfies a reverse Holder inequality. The main idea is to sharpen the well known localization method introduced by Z. Shen. Our results can be regarded as alternative proofs of the boundedness in $H^1$, $L^p$ and $BMO$ of classical $L$-square functions.

math.CA↗