L p l p is bounded for any p 0 pdf available in journal of automated reasoning 541. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields. Polynomial approximation, interpolation, and orthogonal. Hardylittlewoodsobolev inequality without marcinkiewicz interpolation. The interpolation theory was aimed in the two classical theorems. Interpolation, approximation and their applications. Marcinkiewicz type interpolation theorems for weak orlicz martingale spaces. The continuous function curve may characterize the relation between variables x and y more. The interpolation models a set of tabulated function values or discrete data into a continuous function. Intensive program on interpolation and noncommutative. Gilbert on interpolation with change of measure 2, and an extension of a theorem of ben nettdevoresharpley 1. In general this does not hold true in two and more variables. As an application, we prove some martingale inequalities with weak orlicz space norm. Only relatively simple versions of the theorems are treated.
This chapter is devoted to the proofs and some of the applications of the theorems of rieszthorin and of marcinkiewicz, each of which is concerned with operators t defined on subsets of lebesgue spaces constructed over fairly general measure spaces and taking values in similar such spaces. Intuition behind the rieszthorin interpolation theorem. In this section, we focus on employing the technique of atomic decomposition to establish two marcinkiewicz type interpolation theorems for weak orlicz martingale spaces. Here we present the rieszthorin interpolation theorem, the hausdorff. We now prove our results on interpolation theorems on graph parameters. Polynomial approximation, interpolation, and orthogonal polynomials in the last chapter we saw that the eigenequation for a matrix was a polynomial whose roots were the eigenvalues of the matrix. Interpolation theorems on graph parameters 537 theorem 3. Marcinkiewicz interpolation theorem and marcinkiewicz spaces bounded, then it is of strong type p, p, i. The idea of hermite interpolation is clear in the univariate case, namely, when some of the interpolation points coalesce, the interpolating polynomials converge to the hermite interpolation polynomial which interpolates function values and derivatives. This theorem can be used for example, to prove the hausdorffyoung inequality, which establishes that the fourier transform can be extended in a unique way as a continuous linear map.
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