Regularization of Newtonian functions on metric spaces via weak boundedness of maximal operators
Artikel i vetenskaplig tidskrift, 2018

Density of Lipschitz functions in Newtonian spaces based on quasi-Banach function lattices is discussed. Newtonian spaces are first-order Sobolev-type spaces on abstract metric measure spaces defined via (weak) upper gradients. Our main focus lies on metric spaces with a doubling measure that support a Poincaré inequality. Absolute continuity of the function lattice quasi-norm is shown to be crucial for approximability by (locally) Lipschitz functions. The proof of the density result uses, among other facts, the fact that a suitable maximal operator is locally weakly bounded. In particular, various sufficient conditions for such boundedness on quasi-Banach function lattices (and rearrangement-invariant spaces, in particular) are established and applied.

metric measure space

Newtonian space

Sobolev-type space

weak boundedness

rearrangement-invariant space

upper gradient

regularization

Lipschitz function

maximal operator

Banach function lattice

density of Lipschitz functions

Författare

Lukas Maly

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Jyväskylän Yliopisto

Journal dAnalyse Mathematique

0021-7670 (ISSN)

Vol. 134

Ämneskategorier

Matematisk analys

DOI

10.1007/s11854-018-0001-7