On some Fourier aspects of the construction of certain Wiener integrals

The existence and best L2L2-bounds for the Wiener type integrals ∫01f(s)dXs, where XX ranges through a wide class of Bessel-like centered processes, and ff belongs to L2([0,1])L2([0,1]), are discussed in terms of Fourier transforms associated with some characteristics of XX, thus providing some unification of previous results on this topic obtained by the authors [T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered powers of Bessel processes, I, Markov Processes and their Related Fields (2006) (in press), T. Funaki, Y. Hariya, F. Hirsch, M. Yor, On the construction of Wiener integrals with respect to certain pseudo-Bessel processes, Stochastic Processes and their Applications (2006) (in press)] as well as yielding new results.