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Pointwise multiplicative inequalities and Nirenberg type estimates in weighted Sobolev spaces. (English) Zbl 0819.46021

Summary: We prove pointwise multiplicative inequalities on bounded domains with the cone property and on infinite cones, and derive a certain class of multiplicative inequalities in weighted Sobolev spaces with Muckenhoupt weights. We also find some new formulas to represent functions by their derivatives.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
26D10 Inequalities involving derivatives and differential and integral operators
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
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