28 citations · 95 across the 9 of their papers we have counts for
9 papers
Classifying Triebel-Lizorkin capacities in metric spaces
Juha Lehrbäck, Kaushik Mohanta, Antti V. Vähäkangas
We study non-local or fractional capacities in metric measure spaces. Our main goal is to clarify the relations between relative Hajlasz-Triebel-Lizorkin capacities, potentional Tr…
Potential theory and quasisymmetric maps between compact Ahlfors regular metric measure spaces via Besov functions: preliminary
Juha Lehrback, Nageswari Shanmugalingam
We study Besov capacities in a compact Ahlfors regular metric measure space by means of hyperbolic fillings of the space. This approach is applicable even if the space does not sup…
Hardy-Sobolev inequalities and weighted capacities in metric spaces
Lizaveta Ihnatsyeva, Juha Lehrbäck, Antti V. Vähäkangas
Let be an open set in a metric measure space . Our main result gives an equivalence between the validity of a weighted Hardy-Sobolev inequality in and quasiadditivity of…
Fractional Hardy-Sobolev type inequalities for half spaces and John domains
Bartłomiej Dyda, Juha Lehrbäck, Antti V. Vähäkangas
As our main result we prove a variant of the fractional Hardy-Sobolev-Maz'ya inequality for half spaces. This result contains a complete answer to a recent open question by Musina…
Measures with predetermined regularity and inhomogeneous self-similar sets
Antti Käenmäki, Juha Lehrbäck
We show that if is a uniformly perfect complete metric space satisfying the finite doubling property, then there exists a fully supported measure with lower regularity dimensio…
The annular decay property and capacity estimates for thin annuli
Anders Björn, Jana Björn, Juha Lehrbäck
We obtain upper and lower bounds for the nonlinear variational capacity of thin annuli in weighted and in metric spaces, primarily under the assumptions of an annula…
In between the inequalities of Sobolev and Hardy
Juha Lehrbäck, Antti V. Vähäkangas
We establish both sufficient and necessary conditions for the validity of the so-called Hardy-Sobolev inequalities on open sets of the Euclidean space. These inequalities form a na…
Hardy inequalities and Assouad dimensions
Juha Lehrbäck
We establish both sufficient and necessary conditions for weighted Hardy inequalities in metric spaces in terms of Assouad (co)dimensions. Our sufficient conditions in the case whe…
Sharp capacity estimates for annuli in weighted R^n and in metric spaces
Anders Björn, Jana Björn, Juha Lehrbäck
We obtain estimates for the nonlinear variational capacity of annuli in weighted R^n and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all…