In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

In this paper, we proved a weighted Hardy–Rellich inequality for Dunkl operators based on the spherical h-harmonic decomposition theory of operators. Moreover, obtained explicit constant inequalities, which is optimal in some cases. Our results extend known inequalities.

In this paper we extend the classical Bohr’s inequality to setting of non-commutative Hardy space $H^1$ associated with a semifinite von Neumann algebra. As consequence, obtain for operators in Neumann-Schatten class $\mathcal C_1$ and square matrices any finite order. Interestingly, establish that optimal bound $r$ above mentioned concerning is 1/3 whereas it 1/2 case $2\times 2$ reduces $\s...