TY - JOUR
T1 - Boundedness of singular integral operators with variable kernels
AU - Lee, Ming Yi
AU - Lin, Chin Cheng
AU - Lin, Ying Chieh
AU - Yan, Dunyan
N1 - Funding Information:
E-mail addresses: [email protected] (M.-Y. Lee), [email protected] (C.-C. Lin), [email protected] (Y.-C. Lin), [email protected] (D. Yan). 1 Research supported by NSC of Taiwan under Grant #NSC 96-2628-M-008-017. 2 Research supported by NSC of Taiwan under Grant #NSC 96-2115-M-008-002. 3 Research supported by NSF of China under Grants 10571014 and 10631080.
PY - 2008/12/15
Y1 - 2008/12/15
N2 - Let K be a generalized Calderón-Zygmund kernel defined on Rn × (Rn {set minus} {0}). The singular integral operator with variable kernel given byT f (x) = p.v. under(∫, Rn) K (x, x - y) f (y) d y is studied. We show that if the kernel K (x, y) satisfies the Lq-Hörmander condition with respect to x and y variables, respectively, then T is bounded on Lwp. If we add an extra Dini type condition on K, then we may show the Hwp - Lwp boundedness of T.
AB - Let K be a generalized Calderón-Zygmund kernel defined on Rn × (Rn {set minus} {0}). The singular integral operator with variable kernel given byT f (x) = p.v. under(∫, Rn) K (x, x - y) f (y) d y is studied. We show that if the kernel K (x, y) satisfies the Lq-Hörmander condition with respect to x and y variables, respectively, then T is bounded on Lwp. If we add an extra Dini type condition on K, then we may show the Hwp - Lwp boundedness of T.
KW - A weights
KW - L-Dini condition
KW - L-Hörmander condition
KW - Singular integral operators
KW - Variable kernel
UR - http://www.scopus.com/inward/record.url?scp=51249083444&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2008.07.078
DO - 10.1016/j.jmaa.2008.07.078
M3 - 期刊論文
AN - SCOPUS:51249083444
SN - 0022-247X
VL - 348
SP - 787
EP - 796
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -