Equivalence of measures of smoothness in L > p(Sd-1), 1 < p < infinity

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	Equivalence of measures of smoothness in L > p(Sd-1), 1 < p < infinity
	Dai, F. ; Ditzian, Z. ; Huang, Hongwei ; Huang HW(黄宏伟)
刊名	http://dx.doi.org/10.4064/sm196-2-5
	2010
关键词	SPHERE INEQUALITY APPROXIMATION SPACES
英文摘要	NSERC [G121211001, A4816.]; Suppose (Delta) over tilde is the Laplace-Beltrami operator on the sphere S(d-1), Delta(k)(p) f(x) = Delta(p)Delta(k-1)(p)f(x) and Delta(p)f (x) = f(px) - f (x) where p is an element of SO(d). omega(m)(f,t) L(p)(S(d-1)) equivalent to sup{parallel to Delta(m)(p)f parallel to L(p)(S(d-1)) : rho is an element of SO(d), max(x is an element of Sd-1) rho x . x >= cost} and (K) over tilde (m()f,t(m))(p) equivalent to inf{parallel to f - g parallel to L(p)(S(d-1)) + t(m) parallel to(-(Delta) over tilde (m/2)g parallel to L(p)(S(d-1)) : g is an element of D((-(Delta) over tilde)(m/2))} are equivalent for 1 < p < infinity. We note that for even m the relation was recently investigated by the second author. The equivalence yields an extension of the results on sharp Jackson inequalities on the sphere. A new strong converse inequality for L(p)(S(d-1)) given in this paper plays a significant role in the proof.
语种	英语
出版者	STUD MATH
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91050]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Dai, F.,Ditzian, Z.,Huang, Hongwei,et al. Equivalence of measures of smoothness in L > p(Sd-1), 1 < p < infinity[J]. http://dx.doi.org/10.4064/sm196-2-5,2010.
APA	Dai, F.,Ditzian, Z.,Huang, Hongwei,&黄宏伟.(2010).Equivalence of measures of smoothness in L > p(Sd-1), 1 < p < infinity.http://dx.doi.org/10.4064/sm196-2-5.
MLA	Dai, F.,et al."Equivalence of measures of smoothness in L > p(Sd-1), 1 < p < infinity".http://dx.doi.org/10.4064/sm196-2-5 (2010).