Self-improving properties of generalized Orlicz-Poincaré inequalities
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Eriksson-Bique, Sylvester; Lehrbäck, Juha; Vähäkangas, Antti V. (Elsevier BV, 2020)We prove a general self-improvement property for a family of weighted pointwise inequalities on open sets, including pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes ...
Eriksson-Bique, Sylvester; Vähäkangas, Antti V. (American Mathematical Society, 2019)We prove the self-improvement of a pointwise p-Hardy inequality. The proof relies on maximal function techniques and a characterization of the inequality by curves.
Kinnunen, Juha; Lehrbäck, Juha; Vähäkangas, Antti; Zhong, Xiao (Springer Berlin Heidelberg, 2019)Our main result is an estimate for a sharp maximal function, which implies a Keith–Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, ...
Björn, Anders; Björn, Jana; Lehrbäck, Juha (Springer Italia Srl; Universitat de Barcelona, 2017)
Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse (American Institute of Mathematical Sciences (AIMS), 2021)We prove a unique continuation property for the fractional Laplacian (−Δ)s when s∈(−n/2,∞)∖Z where n≥1. In addition, we study Poincaré-type inequalities for the operator (−Δ)s when s≥0. We apply the results to show that ...