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Some integral inequalities with Radon measure. (Chinese. English summary) Zbl 1449.26034

Summary: In this paper, we study the problem of Radon integrability of differential forms satisfying the Dirac-harmonic equation. By two kinds of Hölder inequalities, we first obtain the local Poincaré-type inequality applying to differential forms which satisfy Dirac-harmonic equation. Then, based on the local result, we also obtain the global Poincaré-type inequality on \(\delta \)-John domain by use of some proper integral skills and the property of Whitney cover, which generalized the integral theory in differential form.

MSC:

26D15 Inequalities for sums, series and integrals
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