Corrections to “The maximal function on variable spaces".
The boundedness of classical operators on variable spaces.
Existence and uniqueness results for solutions of nonlinear equations with right hand side in
We prove an existence and uniqueness theorem for the elliptic Dirichlet problem for the equation div a(x,∇u) = f in a planar domain Ω. Here and the solution belongs to the so-called grand Sobolev space . This is the proper space when the right hand side is assumed to be only -integrable. In particular, we obtain the exponential integrability of the solution, which in the linear case was previously proved by Brezis-Merle and Chanillo-Li.
Endpoint estimates and weighted norm inequalities for commutators of fractional integrals.
A New Proof of the Boundedness of Maximal Operators on Variable Lebesgue Spaces
We give a new proof using the classic Calderón-Zygmund decomposition that the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue space whenever the exponent function satisfies log-Hölder continuity conditions. We include the case where assumes the value infinity. The same proof also shows that the fractional maximal operator , , maps into , where .
The fractional maximal operator and fractional integrals on variable spaces.
Page 1