Exact Location of $\a$-Bloch Spaces in $L^p_a$ and $H^p$ of a Complex Unit Ball

Yang, Weisheng; Ouyang, Chuying

doi:10.1216/rmjm/1021477265

Cited by 20 publications

(21 citation statements)

References 12 publications

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“…The same reasoning shows that also

f_{1} \notin {scriptB}_{β}^{\infty}

β < 1

. Applying and Theorem yields

f_{α} \in {scriptB}_{α}^{\infty} ∖ {scriptB}_{< α}^{\infty} false(α \in double-struckR false) .

Further, [, (16) and (17)] say that

f_{< \frac{1 + N}{p}} \in A_{0}^{p} but f_{\frac{1 + N}{p}} \notin A_{0}^{p} .

Finally, applying and Theorem yields as before

f_{< \frac{1 + N + q}{p}} \in B_{q}^{p} but f_{\frac{1 + N + q}{p}} \notin B_{q}^{p} .

We give a proof of simpler than the one in . For

α > 0

, by , for

w = r ζ

with

ζ \in S

and

r \geq 0

, we have

{|f_{α} (w)|}^{p} = \frac{1}{false| 1 - w_{1} |^{α p}} = \frac{1}{false| 1 - false⟨ r ζ, e_{1} false⟩ |^{α p}} <...>

…”

Section: Basic Examplesmentioning

confidence: 76%

See 1 more Smart Citation

Precise inclusion relations among Bergman–Besov and Bloch–Lipschitz spaces and on the unit ball of

Kaptanoğlu

Üreyen

2018

Mathematische Nachrichten

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“…The same reasoning shows that also

f_{1} \notin {scriptB}_{β}^{\infty}

β < 1

. Applying and Theorem yields

f_{α} \in {scriptB}_{α}^{\infty} ∖ {scriptB}_{< α}^{\infty} false(α \in double-struckR false) .

Further, [, (16) and (17)] say that

f_{< \frac{1 + N}{p}} \in A_{0}^{p} but f_{\frac{1 + N}{p}} \notin A_{0}^{p} .

Finally, applying and Theorem yields as before

f_{< \frac{1 + N + q}{p}} \in B_{q}^{p} but f_{\frac{1 + N + q}{p}} \notin B_{q}^{p} .

We give a proof of simpler than the one in . For

α > 0

, by , for

w = r ζ

with

ζ \in S

and

r \geq 0

, we have

{|f_{α} (w)|}^{p} = \frac{1}{false| 1 - w_{1} |^{α p}} = \frac{1}{false| 1 - false⟨ r ζ, e_{1} false⟩ |^{α p}} <...>

…”

Section: Basic Examplesmentioning

confidence: 76%

“…For unweighted Bergman spaces

A_{0}^{p}

, see also [, Proposition 3]. For the spaces

B_{α}^{\infty}

with

α > - 1

, see also [, Proposition 2].

□

…”

Section: Basic Examplesmentioning

confidence: 99%

Precise inclusion relations among Bergman–Besov and Bloch–Lipschitz spaces and on the unit ball of

Kaptanoğlu

Üreyen

2018

Mathematische Nachrichten

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“…To prove that the inclusion is strict, we only need to test functions of the form f t (z) = (1 − z 1 ) t . See Yang-Ouyang [61] for a similar argument.…”

Section: Inclusion Relationsmentioning

confidence: 90%

“…We only give a sketch of the rest of the proof since it is similar to the argument used in Yang-Ouyang [61]. For t > 0 let k be a nonnegative integer such that k + γ > 0.…”

Section: Inclusion Relationsmentioning

confidence: 99%

Theory of Bergman Spaces in the Unit Ball of C^n

Zhao¹,

Zhu²

2008

Mémoires Soc. Math. France

169

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ABSTRACT. There has been a great deal of work done in recent years on weighted Bergman spaces A p α on the unit ball B n of C n , where 0 < p < ∞ and α > −1. We extend this study in a very natural way to the case where α is any real number and 0 < p ≤ ∞. This unified treatment covers all classical Bergman spaces, Besov spaces, Lipschitz spaces, the Bloch space, the Hardy space H 2 , and the so-called Arveson space. Some of our results about integral representations, complex interpolation, coefficient multipliers, and Carleson measures are new even for the ordinary (unweighted) Bergman spaces of the unit disk.

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“…In [5], the Dirichlet type spaces are studied more deeply, and a characterization of BMO type for these spaces is given. The discussion about the function Q p and B p and their relations are given in [2,6,7]. In this paper, the relations between D p and B …”

Section: Introductionmentioning

confidence: 97%

Spaces M(Dp), Bnp, and Qp

2004

Journal of Mathematical Analysis and Applications

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Exact Location of $\a$-Bloch Spaces in $L^p_a$ and $H^p$ of a Complex Unit Ball

Cited by 20 publications

References 12 publications

Precise inclusion relations among Bergman–Besov and Bloch–Lipschitz spaces and on the unit ball of

Precise inclusion relations among Bergman–Besov and Bloch–Lipschitz spaces and on the unit ball of

Theory of Bergman Spaces in the Unit Ball of C^n

Spaces M(Dp), Bnp, and Qp

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