| Co-Investigator(Kenkyū-buntansha) |
UDA Toshio AKITA UNIVERSITY・FACULTY OF EDUCATION AND HUMAN STUDIES,PROFESSOR, 教育文化学部, 教授 (20006589)
SAKA Koichi AKITA UNIVERSITY・FACULTY OF ENGINEERING AND RESOURCE SCIENCE,PROFESSOR, 工学資源学部, 教授 (20006597)
KAWAKAMI Hajime AKITA UNIVERSITY・FACULTY OF ENGINEERING AND RESOURCE SCIENCE,ASSOCIATE PROFESSOR, 工学資源学部, 助教授 (20240781)
ITO Hideji AKITA UNIVERSITY・FACULTY OF EDUCATION AND HUMAN STUDIES,ASSOCIATE PROFESSOR, 教育文化学部, 助教授 (70091783)
FUKUHARA Kenzo AKITA UNIVERSITY・FACULTY OF EDUCATION AND HUMAN STUDIES,ASSOCIATE PROFESSOR, 教育文化学部, 助教授 (00006561)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1998: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1997: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Research Abstract |
Let 2^<omega> be the dyadic group (The Waish-Paley group). 22^<omega> can be identified with the additive group of the ring of integers in the 2-series field K ; i.e., the field of formal Laurent series over GF(2). The Besov space B^<alpha>_<pq> (22^<omega>), 0 < p, q<less than or equal> *, alpha > 0, is the collection of all distribution
f on 22<@D1omega@>D1 such that (SIGMA<@D6*(/)j=0@>D62<@D1qaj@>D1||*<@D2j@>D2 * f||<@D3q(/)Lp(2<@D1omega@>D1))@>D3<@D1<@D71(/)q@>D7 is finite *modification if q=*), where PHI<@D2j@>D2 is the characteristic function of {x : |chi|<less than or equal> 2<@D1j@>D1 and *S1j@>D1(chi)=PHI<@D20@>D2(chi)(j=0), (2<@D1j@>D1PHI<@D2j@>D2-2<@D1J-1@>D1PHI<@D2j-1@>D2)(chi), (j<greater than or equal>1). We have characterized of the Besov space B<@D1alpha@>D1<@D2pq@>D2(2<@D1omega@>D1) by means of the difference, the oscillations, the best approximation and atoms. As one of applications of this characterizations, there is a weak type estimate for the maximal Cesaro means d
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elta<@D1beta@>D1<@D2eta@>D2f on Bdelta<@D1beta@>D1<@D2eta@>D2f(2<@D1omega@>D1). But we have a restriction on the range of p. To show the complete weak type estimate for the full range of siguma, we have studied the decomposition of the Cesaro kernel KAPPA<@D1beta@>D1<@D2pq@>D2(chi) by the finite linear combination of the translation of the characteristic function PHI<@D2j@>D2(x). Also, we have studied the dyadic derivative and the dyadic integral on 2<@D1omega@>D1 which is introduced by Butzer and Wagner. It is shown that Nikol'skij inequality included Bernstein and Markov inequality, Lifting property, related equivalent quasi-norms and some equivalent conditions for the derivative on B<@D1alpha@>D1<@D2pq@>D2. Also we show that the maximal operator of the dyadic derivative of the dyadic integral satisfies the weak type estimate. As a future problem, there are the characterization of B<@D1alpha@>D1<@D2pq@>D2(2<@D1omega@>D1) by the Cesaro means delta<@D1beta@>D1<@D2eta@>D2f, the relations of the strong derivative, weak derivative, Peano derivative and Besov sp Less
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