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A general rearrangement inequality for multiple integrals. (English) Zbl 0286.26005


MSC:

26D15 Inequalities for sums, series and integrals
52A40 Inequalities and extremum problems involving convexity in convex geometry
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[1] Hardy, G. E.; Littlewood, J. E.; Pólya, G., Inequalities (1952), Cambridge University Press: Cambridge University Press London and New York · Zbl 0047.05302
[2] Luttinger, J. M.; Friedberg, R., A New Rearrangement Inequality for Multiple Integrals (1973), Preprint · Zbl 0334.26007
[3] Riesz, F., Sur une Inégalité Intégrale, J. L.M.S., 5, 162-168 (1930) · JFM 56.0232.02
[4] Luttinger, J. M., Generalized isoperimetric inequalities, J. Math. Phys., 14, 1448-1450 (1973) · Zbl 0261.52006
[5] Bonnesen, T.; Fenchel, W., Theorie der Konvexen Körper (1948), Chelsea: Chelsea New York · Zbl 0008.07708
[6] Pólya, G.; Szegö, G., Isoperimetric Inequalities in Mathematical Physics (1951), Princeton Univ. Press: Princeton Univ. Press Princeton · Zbl 0044.38301
[7] Blaschke, W., Kreis und Kugel (1916), Veit and Comp: Veit and Comp Leipzig · JFM 46.1109.01
[8] Hadwiger, H., Vorlesungen über Inhalt, (Oberfläche und Isoperimetrie (1957), Springer: Springer Berlin-Göttingen-Heidelberg) · Zbl 0078.35703
[9] Federer, H., Geometric Measure Theory (1969), Springer: Springer New York · Zbl 0176.00801
[10] Dunford, N.; Schwartz, J. T., Linear Operators (1958), Interscience: Interscience New York and London, Part I
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