Generalized Weighted Sobolev Spaces and Applications to Sobolev Orthogonal Polynomials I

Pseudo-uniform Convexity in Hp and Some Extremal Problems on Sobolev Spaces

“…In the case p ¼ 2, the polynomials fP n g n¼0, 1,... are usually said to be Sobolev orthogonal polynomials. The special case k ¼ 1 has been studied by many authors (see, for instance [10,12,18]). For k ¼ 0 we have the classical orthogonality.…”

“…[18]. On the other side is the characterization of H p ðÞ for 2 S. The following theorem is very well known but we only found a reference for 1 p 1 (see [5] and page 22 in [16]).…”

Measurable diagonalization of positive definite matrices

“…In [1,3,[13][14][15][16][17] there are some answers to the question stated in [8] about some conditions for M to be bounded: the more general result on this topic is [1, Theorem 8.1] which characterizes in a simple way (in terms of equivalent norms in Sobolev spaces) the boundedness of M for the classical diagonal case…”

The Multiplication Operator, Zero Location and Asymptotic for Non-diagonal Sobolev Norms

“…In [27], [28], [29] and [30] the authors developed a theory of general Sobolev spaces with respect to measures in the real line, in order to apply it to the study of Sobolev orthogonal polynomials.…”

“…In [1], [28], [30], [31] and [32], there are some answers to the question stated in [21] about some conditions for M to be bounded: the more general result on this topic is [1, Theorem 8.1] which characterizes in a simple way (in terms of equivalent norms in Sobolev spaces) the boundedness of M for the classical "diagonal" case…”