Li, Huacan; Li, Qunfang Some integral inequalities with Radon measure. (Chinese. English summary) Zbl 1449.26034 J. Math., Wuhan Univ. 39, No. 6, 899-906 (2019). 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 Keywords:Dirac-harmonic equation; integral inequalities; Radon measure PDFBibTeX XMLCite \textit{H. Li} and \textit{Q. Li}, J. Math., Wuhan Univ. 39, No. 6, 899--906 (2019; Zbl 1449.26034) Full Text: DOI