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- W32330635 abstract "Density of Lipschitz functions in Newtonian spaces based on quasi-Banach function lattices is discussed. Newtonian spaces are first-order Sobolevtype 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." @default.
- W32330635 created "2016-06-24" @default.
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- W32330635 date "2018-02-01" @default.
- W32330635 modified "2023-10-12" @default.
- W32330635 title "Regularization of Newtonian functions on metric spaces via weak boundedness of maximal operators" @default.
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- W32330635 doi "https://doi.org/10.1007/s11854-018-0001-7" @default.
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