Sharp weighted fractional Hardy inequalities
Volume 274 / 2024
Studia Mathematica 274 (2024), 153-171
MSC: Primary 46E35; Secondary 39B72, 26D15
DOI: 10.4064/sm230109-4-9
Published online: 3 January 2024
Abstract
We investigate the weighted fractional order Hardy inequality for \Omega =\mathbb R ^{d-1}\times (0,\infty ), \Omega being a convex domain or \Omega =\mathbb R ^d\setminus \{0\}. Our work focuses on finding the best (i.e. sharp) constant C=C(d,s,p,\alpha ,\beta ) in all cases. We also obtain a weighted version of the fractional Hardy–Sobolev–Maz’ya inequality. The proofs are based on general Hardy inequalities and the nonlinear ground state representation, established by Frank and Seiringer.
