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Oscillation estimates, self-improving results and good-$lambda$ inequalities | | Lauri Berkovits
; Juha Kinnunen
; José María Martell
; | | Date: |
9 Jul 2015 | | Abstract: | Our main result is an abstract good-$lambda$ inequality that allows us to
consider three self-improving properties related to oscillation estimates in a
very general context. The novelty of our approach is that there is one
principle behind these self-improving phenomena. First, we obtain higher
integrability properties for functions belonging to the so-called
John-Nirenberg spaces. Second, and as a consequence of the previous fact, we
present very easy proofs of some of the self-improving properties of the
generalized Poincar’e inequalities studied by B. Franchi, C. P’erez and R.
Wheeden, and by P. MacManus and C. P’erez . Finally, we show that a weak
Gurov-Reshetnyak condition implies higher integrability with asymptotically
sharp estimates. We discuss these questions both in Euclidean spaces with
dyadic cubes and in spaces of homogeneous type with metric balls. We develop
new techniques that apply to more general oscillations than the standard mean
oscillation and to overlapping balls instead of dyadic cubes. | | Source: | arXiv, 1507.2398 | | Services: | Forum | Review | PDF | Favorites | |
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