학술저널
NOTES ON THE SPACE OF DIRICHLET TYPE AND WEIGHTED BESOV SPACE
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 26, No. 2
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2013.05393 - 402 (10 pages)
- 2
For 0 < p < 1, ？？ > ¡1 and 0 < r < 1, we show thatif f is in the space of Dirichlet type Dp p¡1, then R 1 0 Mpp (r; f0)(1 ¡r)p¡1rdr < 1 andR 1 0 M(2+？？)p(2+？？)p (r; f0)(1¡r)(2+？？)p+？？rdr < 1 where Mp(r; f) =h12¼ R 2¼ 0 jf(reit)jpdt i1=p: For 1 < p < q < 1 and ？？ + 1 < p, we show that if there exists some positive constant c such that k f kLq(d¹)· c k f kDp？？ for all f 2 Dp？？, then k f kLq(d¹)· c k f kBp(g) where Bp(g) is the weighted Besov space. We also ¯nd the condition of measure ¹ such that supa2D RD(ka(z)(1 ¡jaj2)(p¡？閻？1))q=pd¹(z) < 1:
1. Introduction
2. Properties of Mp(r; f)
3. Space of Dirichlet type and weighted Besov space
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