Estimates of Derivatives in Sobolev Spaces in Terms of Hypergeometric Functions.

The paper deals with sharp estimates of derivatives of intermediate order in the Sobolev space , . The functions under study are the smallest possible quantities in inequalities of the form The properties of the primitives of shifted Legendre polynomials on the interval are used to obtain an explicit description of these functions in terms of hypergeometric functions. In the paper, a new relation connecting the derivatives and primitives of Legendre polynomials is also proved. [ABSTRACT FROM AUTHOR]