紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2025, 62(4), p. 587-608

L^p - L^q ESTIMATES FOR SUBELLIPTIC PSEUDO-DIFFERENTIAL OPERATORS ON COMPACT LIE GROUPS

Departments of Mathematics, The University of Osaka and Osaka Metropolitan University

英語

text

2025-10

We establish the L^p-L^q-boundedness of subelliptic pseudo-differential operators on a compact Lie group G. Effectively, we deal with the L^p-L^q-bounds for operators in the sub-Riemmanian setting because the subelliptic classes are associated to a Hörmander sub-Laplacian. The Riemannian case associated with the Laplacian is also included as a special case. Then, applications to the L^p-L^q-boundedness of pseudo-differential operators in the Hörmander classes on G are given in the complete range 0 ≤ δ ≤ ρ ≤ 1, δ < 1. This also gives the L^p-L^q-bounds in the Riemannian setting, because the later classes are associated with the Laplacian on G. In both cases, in the Riemannian and the sub-Riemannian settings, necessary and sufficient conditions for the L^p-L^q-boundedness of operators are also analysed.

10.18910/102979

102979

L^p - L^q ESTIMATES FOR SUBELLIPTIC PSEUDO-DIFFERENTIAL OPERATORS ON COMPACT LIE GROUPS

Departments of Mathematics, The University of Osaka and Osaka Metropolitan University

英語

2025-10

Osaka Journal of Mathematics

62

4

587

608

https://hdl.handle.net/11094/102979

10.18910/102979

https://doi.org/10.18910/102979