Weighted Discrete Hardy Inequalities on Trees and Applications

In this paper, we study certain inequalities and a related result for weighted Sobolev spaces on Hölder-α domains, where the weights are powers of distance to boundary. We obtain results regarding divergence equation’s solvability, improved Poincaré, fractional Korn inequalities. The proofs based local-to-global argument that involves kind atomic decomposition functions validity discrete Hardy-type inequality trees. novelty our approach lies in use Hardy sufficient condition allows us interest. As consequence, assumptions weight exponents appear weaker than those literature.