We study Besov and Triebel–Lizorkin space estimates for fractional diffusion. We measure the smoothing effect of the fractional heat flow in terms of the Besov and Triebel–Lizorkin scale. These estimates have many applications to various partial differential equations.
Bibliographical noteFunding Information:
K. Yabuta was supported partly by Grant-in-Aid for Scientific Research (C) No. 15K04942, Japan Society for the Promotion of Science. M. Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1C1B2015731). 2010 Mathematics Subject Classification. Primary 42B25; Secondary 26D10. Key words and phrases. Fractional di¤usion, Besov spaces, Triebel–Lizorkin spaces.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology