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An approximate gradient and Sobolev derivatives. (Russian. English summary) Zbl 1144.49303

Summary: Approximate gradient is presented as convolution operator of investigated function and some weight function. Special definition of weight function makes it possible to consider the approximate gradient as the class of integral transformations such as Riesz transformation, gradients of Bessel potentials and Poisson integral. It is shown that the averages under Steklov the Sobolev’s derivatives are such transformations.

MSC:

49J52 Nonsmooth analysis
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems