In this paper, we shall introduce the concept of the Bessel （Riesz） potential Kothe function spaces X<sup>s</sup> （<sup>s</sup>） and give some dual estimates for a class of operators determ...In this paper, we shall introduce the concept of the Bessel （Riesz） potential Kothe function spaces X<sup>s</sup> （<sup>s</sup>） and give some dual estimates for a class of operators determined by a semi-group in the spaces L<sup>q</sup> （-T, T; X<sup>s</sup>） （L<sup>q</sup>（-T, T; <sup>s</sup> ））. Moreover, some time-space L<sup>P</sup>-L<sup>P</sup><sup> </sup>estimates for the semi-group exp(it（-△）<sup>m/2</sup>) and the operator A:=∫<sub>0</sub><sup>t</sup> exp(i（t-τ）（-△）<sup>m/2</sup>). dτ in the Lebesgue-Besov spaces L<sup>q</sup>(-T, T; <sub>p,2</sub><sup>S</sup>) are given. On the basis of these results, in a subsequent paper we shall present some further applications to a class of nonlinear wave equations.展开更多
基金Supported in part by the Doctoral Research Foundation of Hebei Province
文摘In this paper, we shall introduce the concept of the Bessel （Riesz） potential Kothe function spaces X<sup>s</sup> （<sup>s</sup>） and give some dual estimates for a class of operators determined by a semi-group in the spaces L<sup>q</sup> （-T, T; X<sup>s</sup>） （L<sup>q</sup>（-T, T; <sup>s</sup> ））. Moreover, some time-space L<sup>P</sup>-L<sup>P</sup><sup> </sup>estimates for the semi-group exp(it（-△）<sup>m/2</sup>) and the operator A:=∫<sub>0</sub><sup>t</sup> exp(i（t-τ）（-△）<sup>m/2</sup>). dτ in the Lebesgue-Besov spaces L<sup>q</sup>(-T, T; <sub>p,2</sub><sup>S</sup>) are given. On the basis of these results, in a subsequent paper we shall present some further applications to a class of nonlinear wave equations.
