Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Integral transforms and operational calculus

The Boundedness of Multilinear Integer Operator

Author LvZhiJun
Tutor LiuZuo
School Hunan University
Course Basic mathematics
Keywords Multilinear integer operators BMO space Hardy space Herz space Herz - Hardy space Triebel - Lizorkin space Lipschitz space
CLC O177.6
Type Master's thesis
Year 2007
Downloads 35
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In this paper, we study the boundedness of the multilinear integer operators ,i.e., we study the boundedness of multilinear integer operators generated by BMO functions, Osc functions or Lipschitz functions on Lp(1 < p <∞) space、Hardy spaceHerz - Hardy space and Triebel - Lizorkin space.At first, the sharp inequalities for the multilinear integer operators gener ated by Osc functions are proved. By using it, we obtain TA(f) are bounded on Lp(ω)(1 < p <∞) space and weak Llog L space.After that, the boundedness for the multilinear integer operators generated by BMO functions on HDmAp(Rn) space and H(?)q,DmAα,p(Rn) space are proved, where Dm A∈BMO(Rn), |β|=mi, 1≤i≤l. In fact, it is also bounded on HKq,DmAα,p(Rn) space.Then, we get that the multilinear integer operators generated by Lipschitz functions are bounded from LP(Rn) to (?)plβ,∞(Rn), where 1 < p <∞, and LP(Rn) to Lq(Rn), where 1/p - 1/q = lβ/n and 1 < p < lβ/n.

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