On some Fourier aspects of the construction of certain Wiener integrals

The existence and best L 2 -bounds for the Wiener type integrals ∫ 0 1 f ( s ) d X s , where X ranges through a wide class of Bessel-like centered processes, and f belongs to L 2 ( [ 0 , 1 ] ) , are discussed in terms of Fourier transforms associated with some characteristics of X , 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.