END-POINT WEAK BOUNDEDNESS OF SOME POLYNOMIAL-EXPANSIONS

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:49

Article

GUADALUPE, JJ ; PEREZ, M ; RUIZ, FJ ; VARONA, JL

关键词: FOURIER-JACOBI SERIES;    WEAK BOUNDEDNESS;    ORTHOGONAL POLYNOMIALS;   

DOI  :  10.1016/0377-0427(93)90139-3

来源: Elsevier

【 摘 要 】

Let w(x) = (1 - x)alpha(1 + x)beta on [-1, 1], alpha,beta greater-than-or-equal-to -1/2, and for each function f let S(n)f be the nth expansion in the corresponding orthonormal polynomials. We show that the operators f --> uS(n)(u-1f) are not of weak (p, p)-type, where u is another Jacobi weight and p is an endpoint of the interval of mean convergence. The same result is shown for expansions associated to measures of the form dnu = w(x) dx + SIGMA(i=1)(k)M(i)delta(alpha(i)).

【 授权许可】

Free