Conductor inequalities and criteria for Sobolev-Lorentz two-weight inequalities

Details Conductor inequalities and criteria for Sobolev-Lorentz two-weight inequalities Conductor inequalities and criteria for Sobolev-Lorentz two-weight inequalities

2008-04-18

arxiv.org/abs/0804.3051v1

Mathematics

Analysis of PDEs

v1: 15 pages

Scientific paper

In this paper we present integral conductor inequalities connecting the Lorentz p,q-(quasi)norm of a gradient of a function to a one-dimensional integral of the p,q-capacitance of the conductor between two level surfaces of the same function. These inequalities generalize an inequality obtained by the second author in the case of the Sobolev norm. Such conductor inequalities lead to necessary and sufficient conditions for Sobolev-Lorentz type inequalities involving two arbitrary measures.

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