A note on Marcinkiewicz integrals supported by submanifolds

作者：Liu, Feng^*

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2018, 2018(1): 228.

DOI：10.1186/s13660-018-1822-8

• Polynomial compound mappings
• H-1(Sn-1)
• Triebel-Lizorkin spaces
• Besov spaces

In the present paper, we establish the boundedness and continuity of the parametric Marcinkiewicz integrals with rough kernels associated to polynomial mapping P as well as the corresponding compound submanifolds, which is defined by
M(h,Omega,P)(rho)f(x) = (integral(infinity)(0)vertical bar 1/t(rho) integral(vertical bar y vertical bar <= t) Omega(y)h(vertical bar y vertical bar)/vertical bar y vertical bar(n-rho)f(x - P(y)) dy vertical bar(2)dt/t)(1/2),
on the Triebel-Lizorkin spaces and Besov spaces when Omega is an element of H-1(Sn-1) and h is an element of Delta(gamma) (R+) for some gamma > 1. Our main results represent significant improvements and natural extensions of what was known previously.

• 出版日期2018-9-4
• 单位山东科技大学