On W-1,W-p-convergence of Fourier-Sobolev expansions Articles uri icon

publication date

  • February 2012

start page

  • 594

end page

  • 599

volume

  • 398

international standard serial number (ISSN)

  • 0022-247X

electronic international standard serial number (EISSN)

  • 1096-0813

abstract

  • Let {q(n)}(n >= 0) be the sequence of polynomials orthonormal with respect to the Sobolev inner product < f, g > s := f(-1)(1)f(x)fg(x)w(0)(x)dx + f(-1)(1)f'(x)g'(x)w(1)(x)dx, where w(0) is an element of L-infinity ([-1, 1]) and w(1) is a weight of Kufner-Opic type. We study necessary and/or sufficient conditions for the convergence in the W-1,W-p([-1, 1], (w(0), w(1))) norm of the Fourier expansion in terms of {q(n))(n >= 0), with 1 < p < infinity. (C) 2012 Elsevier Inc. All rights reserved.