Integral means for the first derivative of Blaschke products
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概要
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Suppose that <I>B</I>(<I>z</I>, {<I>a</I><SUB><I>k</I></SUB>}) is a Blaschke product associated with the sequence {<I>a</I><SUB><I>k</I></SUB>}. If ∑<SUB><I>k</I>=1</SUB><SUP>∞</SUP>(1−<I>|a</I><SUB><I>k</I></SUB><I>|</I>)<SUP>α</SUP><∞ for some α in (0, 1/2), it is known that <I>B'</I>(<I>z</I>, {<I>a</I><SUB><I>k</I></SUB>})∈<I>H</I><SUP><I>p</I></SUP> for all <I>p</I> in (0, 1−α]. We extend this result by considering the situation when <I>p</I>>1−α. In these cases we obtain that <I>B'</I>(<I>z</I>, {<I>a</I><SUB><I>k</I></SUB>})∉<I>H</I><SUP><I>p</I></SUP>. We then give some counterexamples to indicate to what extent our results may be regarded as being best possible.
- 国立大学法人 東京工業大学大学院理工学研究科数学専攻の論文
国立大学法人 東京工業大学大学院理工学研究科数学専攻 | 論文
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