Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces
UDC 517.5 The higher-order commutators of  fractional Hardy-type operators  of variable order $\zeta(z)$ are shown to be bounded from the  grand variable  Herz spaces ${\dot{K} ^{a(\cdot), u),\theta}_{ p(\cdot)}(\mathbb{R}^n)}$ into the weighted sp...
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| Datum: | 2024 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2024
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7546 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.5
The higher-order commutators of  fractional Hardy-type operators  of variable order $\zeta(z)$ are shown to be bounded from the  grand variable  Herz spaces ${\dot{K} ^{a(\cdot), u),\theta}_{ p(\cdot)}(\mathbb{R}^n)}$ into the weighted space ${\dot{K} ^{a(\cdot), u),\theta}_{\rho, q(\cdot)}(\mathbb{R}^n)},$ where $\rho=(1+|z_1|)^{-\lambda}$ and $\displaystyle {1 \over q(z)}={1 \over p(z)}-{\zeta (z) \over n}$ if $p(z)$ is not necessarily constant at infinity. |
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| DOI: | 10.3842/umzh.v76i7.7546 |