We revisit the Rellich inequality from the viewpoint of isolating the contributions from radial
and spherical derivatives. This naturally leads to a comparison of the norms of the radial …

We establish improved Hardy inequalities for the magnetic p-Laplacian due to adding
nontrivial magnetic fields. We also prove that for Aharonov–Bohm magnetic fields the sharp …

We investigate the improvements of the L p-Hardy and L p-Rellich inequalities when adding
a large class of magnetic fields. In particular, under certain conditions of the magnetic …

We analyse the energy supercritical semilinear wave equation $$\Phi_ {tt}-\Delta\Phi-
|\Phi|^{p-1}\Phi= 0$$ in $\mathbb R^ d $ space. We first prove in a suitable regime of …

We prove uniform resolvent estimates in weighted $ L^ 2$-spaces for radial solutions of the
sublaplacian $\mathcal {L} $ on the Heisenberg group $\mathbb {H}^ d $. The proofs are …

FRACTIONAL HARDY-RELLICH INEQUALITIES VIA A POHOZAEV IDENTITY 1. Introduction
In [35], GH Hardy proved that, if p > 1 and Page 1 FRACTIONAL HARDY-RELLICH …

When studying the weighted Hardy-Rellich inequality in $ L^ 2$ with the full gradient
replaced by the radial derivative the best constant becomes trivially larger or equal than in …

In this paper, we proved a weighted Hardy–Rellich inequality for Dunkl operators based on
the spherical h-harmonic decomposition theory of Dunkl operators. Moreover, we obtained …

The motive of this note is twofold. Inspired by the recent development of a new kind of Hardy
inequality, here we discuss the corresponding Hardy-Rellich and Rellich inequality versions …

In this paper, we provide sufficient conditions for the functions\(\psi\) and\(\phi\) to be the
approximate duals in the Hardy space\(H^ p (\mathbb {R})\) for all\(0< p\le 1\). Based on …