Vanishing generalized Orlicz-Morrey spaces and fractional maximal operator

Deringoz, Fatih; Guliyev, Vagif S.; Samko, Stefan

http://hdl.handle.net/10400.1/13343

Use this identifier to reference this record.

Name:	Description:	Size:	Format:
load_pdf.pdf		448.39 KB	Adobe PDF	Download

Send Feedback

Authors

Deringoz, Fatih

Guliyev, Vagif S.

Samko, Stefan

Abstract(s)

We find sufficient conditions for the non-triviality of the generalized Orlicz-Morrey spaces M-Phi,M-phi (R-n), and prove the boundedness of the fractional maximal operator and its commutators with BMO-coefficients in vanishing generalized Orlicz-Morrey spaces VM Phi,phi (R-n) including weak versions of these spaces. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators involving the Young functions Phi(u), Psi(u) and the function phi(x,r) defining the space. No kind of monotonicity condition on phi(x,r) in r is imposed.