Two-weight boundedness for local fractional maximal and applications

RAMSEYER, MAURICIO; SALINAS, OSCAR; TOSCHI, MARISA

European Journal of Mathematics

Springer

Año: 2023 vol. 9

2199-675X

Given $\Omega$ a proper open subset of a metric space with the weak homogeneity property and a measure $\mu$ doubling on certain local balls, we give sufficient conditions about local weights for the two-weight boundedness of the local fractional maximal operator acting on weighted Lebesgue spaces. As applications we obtain analogous results for singular and fractional type operators and their commutators. As a further application we present an a priori estimate for solutions of $\Delta^mu=f$ in $\Omega$, acting in weighted Sobolev spaces involving the distance to the boundary and different local weights.