An estimate for the L2-norm of a quasi continuous function with respect to a smooth measure

摘要

1. Introduction. Let A be a nonnegative Radon measure on W1, d 3: 3. The following inequality is proved in [4]: There exists an Md > 0 such that for any quasi continuous function u eif'tf) (where H1 (Rd) is the Sobolev space), This inequality was fundamental for establishing results in the above mentioned paper, and has attracted some interest.