TY - JOUR
T1 - Sharp estimates for pseudo-differential operators of type (1,1) on Triebel–Lizorkin and Besov spaces
AU - Park, Bae Jun
N1 - Publisher Copyright:
© Instytut Matematyczny PAN, 2020.
PY - 2020
Y1 - 2020
N2 - Pseudo-differential operators of type (1, 1) and order m are continuous from Fps+m,q to Fps,q if s > d/min (1, p, q) - d for 0 < p < ∞, and from Bps+m,q to Bps,q if s > d/min (1, p) - d for 0 < p ≤ ∞. In this work we extend the F-boundedness result to p = ∞. Additionally, we prove that the operators map F∞m,1 into bmo when s = 0, and consider Hörmander’s twisted diagonal condition for arbitrary s ∈ R. We also prove that the restrictions on s are necessary for the boundedness to hold.
AB - Pseudo-differential operators of type (1, 1) and order m are continuous from Fps+m,q to Fps,q if s > d/min (1, p, q) - d for 0 < p < ∞, and from Bps+m,q to Bps,q if s > d/min (1, p) - d for 0 < p ≤ ∞. In this work we extend the F-boundedness result to p = ∞. Additionally, we prove that the operators map F∞m,1 into bmo when s = 0, and consider Hörmander’s twisted diagonal condition for arbitrary s ∈ R. We also prove that the restrictions on s are necessary for the boundedness to hold.
KW - Pseudo-differential operator
KW - Triebel–Lizorkin spaces
UR - https://www.scopus.com/pages/publications/85092783697
U2 - 10.4064/sm180317-25-11
DO - 10.4064/sm180317-25-11
M3 - Article
AN - SCOPUS:85092783697
SN - 0039-3223
VL - 250
SP - 129
EP - 162
JO - Studia Mathematica
JF - Studia Mathematica
IS - 2
ER -