A maximal Function Approach to Two-Measure Poincaré Inequalities

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

Organisaatiot

  • University of Jyväskylä

Kuvaus

This paper extends the self-improvement result of Keith and Zhong in Keith and Zhong (Ann. Math. 167(2):575–599, 2008) to the two-measure case. Our main result shows that a two-measure (p, p)-Poincaré inequality for 1 < p< ∞ improves to a (p, p- ε) -Poincaré inequality for some ε> 0 under a balance condition on the measures. The corresponding result for a maximal Poincaré inequality is also considered. In this case the left-hand side in the Poincaré inequality is replaced with an integral of a sharp maximal function and the results hold without a balance condition. Moreover, validity of maximal Poincaré inequalities is used to characterize the self-improvement of two-measure Poincaré inequalities. Examples are constructed to illustrate the role of the assumptions. Harmonic analysis and PDE techniques are used extensively in the arguments.

Yksityiskohdat

AlkuperäiskieliEnglanti
JulkaisuJOURNAL OF GEOMETRIC ANALYSIS
TilaSähköinen julkaisu (e-pub) ennen painettua julkistusta - 2018
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 31918033