Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0538.47020
Sawyer, Eric
Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator. (English)
[J] Trans. Am. Math. Soc. 281, 329-337 (1984). ISSN 0002-9947; ISSN 1088-6850/e

Let f(x) denote a measurable function defined on $(0,\infty)$. The Hardy operator T is defined by $Tf(x)=\int\sp{x}\sb{0}f(s)ds.$ Suppose w(x) and v(x) are nonnegative weight functions. \par What conditions for the pair of w,v are necessary and sufficient in order that the operator T will be bounded from the Lorentz space $L\sp{r,s}((o,\infty),vdx)$ to $L\sp{p,q}((o,\infty),wdx) (o<p,q,r,s\le \infty)?$ \par This is the problem discussed in this paper. The modified Hardy operators $T\sb{\eta}f(x)=x\sp{-\eta}Tf(x)$ for $\eta$ real are also treated.
[K.Wang]

MSC 2000:: *47B38 Operators on function spaces
46E30 Spaces of measurable functions
47A30 Operator norms and inequalities

Keywords: weight; Lorentz space; norm inequalities; Hardy operator

Cited in: Zbl 0813.47033

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]