Sharp estimates for the norms of Hardy-type operators on the cones of quasimonotone functions (Q2783071)
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scientific article; zbMATH DE number 1729320
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sharp estimates for the norms of Hardy-type operators on the cones of quasimonotone functions |
scientific article; zbMATH DE number 1729320 |
Statements
9 February 2004
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Hardy operators
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non-negative monotone functions
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Sharp estimates for the norms of Hardy-type operators on the cones of quasimonotone functions (English)
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The author presents a two-sided estimate of the norm of the restriction of the generalized Hardy operators NEWLINE\[NEWLINEA_{r,\mu}f(t)=\Biggl(\int_0^t f^r d\mu\Biggr)^{\frac 1{r}},\quad B_{r,\mu}f(t)=\Biggl(\int_t^{\infty} f^r d\mu\Biggr)^{\frac 1{r}}NEWLINE\]NEWLINE to the cone of non-negative monotone functions \(\Omega_k=\{f\geq 0: f(t)k(t)^{-1}\uparrow\}\) via the involved weights \(\mu\) and \(k\).NEWLINENEWLINEFor the entire collection see [Zbl 0981.00017].
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