Poincaré inequalities for the maximal function
Copyright policy )Poincaré inequalities for the maximal function
We study generalized Poincar�� inequalities. We prove that if a function satisfies a suitable inequality of Poincar�� type, then the Hardy-Littlewood maximal function also obeys a meaningful estimate of similar form. As a by-product, we get a unified approach to proving that the maximal operator is bounded on Sobolev, Lipschitz and BMO spaces.
19 pages, 1 figure, a change in the abstract and a mistake removed. The application to $W^{1,1}$ reproduces the known results but does not improve them. All theorems remain as they were
- Aalto University Finland
ta113, 42B25, 46E35, 42B35, Mathematics - Classical Analysis and ODEs, ta111, Classical Analysis and ODEs (math.CA), FOS: Mathematics
ta113, 42B25, 46E35, 42B35, Mathematics - Classical Analysis and ODEs, ta111, Classical Analysis and ODEs (math.CA), FOS: Mathematics
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