END-POINT WEAK BOUNDEDNESS OF SOME POLYNOMIAL-EXPANSIONS

[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)).

[发布日期] 1993-12-31

[关键词] FOURIER-JACOBI SERIES;WEAK BOUNDEDNESS;ORTHOGONAL POLYNOMIALS