Improved Sobolev regularity for linear nonlocal equations with VMO coefficients

Abstract This work is concerned with both higher integrability and differentiability for linear nonlocal equations possibly very irregular coefficients of VMO-type or even that are merely small in BMO. In particular, such might be discontinuous. While corresponding local elliptic VMO a gain Sobolev regularity along the scale unattainable, it was already observed previous works gaining our setting possible under less restrictive assumptions than setting. this paper, we follow direction show on right-hand side allow an arbitrarily integrability, weak solutions $$u \in W^{s,2}$$ u ∈ W s , 2 fact belong to $$W^{t,p}_{loc}$$ loc t p any $$s \le t < \min \{2s,1\}$$ ≤ < min { 1 } , where $$p>2$$ > reflects amount gained. other words, does not depend able gain. extends numerous results works, either continuity coefficient required only general smaller proved.