## Taiwanese Journal of Mathematics

### BOUNDEDNESS OF SUBLINEAR OPERATORS IN HERZ-TYPE HARDY SPACES

Yuan Zhou

#### Abstract

Let $p\in(0,1]$, $q\in(1,\infty)$, $\alpha\in[n(1-1/q),\infty)$ and $w_1,\,w_2\in A_1$. The author proves that the norms in weighted Herz-type Hardy spaces $HK^{\alpha,\,p}_q(w_1,\,w_2)$ and $HK^{\alpha,\,p}_q(w_1,\,w_2)$ can be achieved by finite central atomic decompositions in some dense subspaces of them. As an application, the author proves that if $T$ is a sublinear operator and maps all central $(\alpha,\, q,\,s;\,w_1,\,w_2)_0$-atoms (resp. central $(\alpha,\, q,\,s;\,w_1,\,w_2)$-atoms of restrict type) into uniformly bounded elements of certain quasi-Banach space $\cal B$ for certain nonnegative integer $s$ no less than the integer part of $\alpha-n(1-1/q)$, then $T$ uniquely extends to a bounded operator from $H\dot K^{\alpha,\,p}_q(w_1,\,w_2)$ (resp. $HK^{\alpha,\, p}_q(w_1,\,w_2)$) to $\cal B$.

#### Article information

Source
Taiwanese J. Math., Volume 13, Number 3 (2009), 983-996.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405453

Digital Object Identifier
doi:10.11650/twjm/1500405453

Mathematical Reviews number (MathSciNet)
MR2526352

Zentralblatt MATH identifier
1180.42009

#### Citation

Zhou, Yuan. BOUNDEDNESS OF SUBLINEAR OPERATORS IN HERZ-TYPE HARDY SPACES. Taiwanese J. Math. 13 (2009), no. 3, 983--996. doi:10.11650/twjm/1500405453. https://projecteuclid.org/euclid.twjm/1500405453

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