83 citations · 183 across the 10 of their papers we have counts for
10 papers
Weakly porous sets and Muckenhoupt distance functions
Theresa C. Anderson, Juha Lehrbäck, Carlos Mudarra +1
We examine the class of weakly porous sets in Euclidean spaces. As our first main result we show that the distance weight belongs to the Mucken…
Capacities and density conditions in metric spaces
Javier Canto, Lizaveta Ihnatsyeva, Juha Lehrbäck +1
We examine the relations between different capacities in the setting of a metric measure space. First, we prove a comparability result for the Riesz -capacity and the relati…
Volume growth, capacity estimates, -parabolicity and sharp integrability properties of -harmonic Green functions
Anders Björn, Jana Björn, Juha Lehrbäck
In a complete metric space equipped with a doubling measure supporting a -Poincaré inequality, we prove sharp growth and integrability results for -harmonic Green functions a…
Uniqueness of diffusion on domains with rough boundaries
Juha Lehrbäck, Derek W. Robinson
Let be a domain in and a quadratic form on with domain where the are real…
Fractional Hardy inequalities and visibility of the boundary
Lizaveta Ihnatsyeva, Juha Lehrbäck, Heli Tuominen +1
We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditio…
Fractional maximal functions in metric measure spaces
Toni Heikkinen, Juha Lehrbäck, Juho Nuutinen +1
We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying…
Quasiadditivity of variational capacity
Juha Lehrbäck, Nageswari Shanmugalingam
We study the quasiadditivity property (a version of superadditivity with a multiplicative constant) of variational capacity in metric spaces with respect to Whitney type covers. We…
Weighted Hardy inequalities beyond Lipschitz domains
Juha Lehrbäck
It is a well-known fact that in a Lipschitz domain Ω\subset R^n a p-Hardy inequality, with weight d(x,\partialΩ)^β, holds for all u\in C_0^\infty(Ω) whenever β<p-1. We show that ac…
Dimensions, Whitney covers, and tubular neighborhoods
Antti Käenmäki, Juha Lehrbäck, Matti Vuorinen
Working in doubling metric spaces, we examine the connections between different dimensions, Whitney covers, and geometrical properties of tubular neighborhoods. In the Euclidean sp…
The equivalence between pointwise Hardy inequalities and uniform fatness
Riikka Korte, Juha Lehrbäck, Heli Tuominen
We prove an equivalence result between the validity of a pointwise Hardy inequality in a domain and uniform capacity density of the complement. This result is new even in Euclidean…