5 papers
Beyond local maximal operators
Hannes Luiro, Antti V. Vähäkangas
We obtain (essentially sharp) boundedness results for certain generalized local maximal operators between fractional weighted Sobolev spaces and their modifications. Concrete bound…
On the Local Theorem under Minimal Integrability
Michael T Lacey, Antti V Vähäkangas
We prove a version of the local Tb Theorem assuming that the accretive functions b_Q and T b_Q are locally L ^{p} integrable, for any 1< p < \infty . This improves a recent result…
Fractional Hardy-type inequalities in domains with plump complement
David E. Edmunds, Ritva Hurri-Syrjänen, Antti V. Vähäkangas
We establish fractional Hardy-type inequalities in a bounded domain with plump complement. In particular our results apply in bounded C^\infty domains and Lipschitz domains.
A T1 theorem for weakly singular integral operators
Antti V. Vähäkangas
We establish conditions in the spirit of the T1 theorem of David and Journé which guarantee the boundedness of \nabla T on L^p(\R^n), where T is an integral transformation and 1<p<…
On extension of Green's operator on bounded smooth domains
Antti Vähäkangas
We prove a regularity result for Green's functions that are associated to elliptic second order divergence-type linear PDO's with coefficients in C^{1,α}(\barΩ). Here α\in (0,1) an…