Integral analog of one generalization of the Hardy inequality and its applications
Under certain conditions on continuous functions $μ, λ, a$, and $f$, we prove the inequality $$\int\limits_0^y {\mu (x)\lambda (x)f\left( {\frac{{\int_0^x {\lambda (t)a(t)dt} }}{{\int_0^x {\lambda (t)dt} }}} \right)dx \leqslant K\int\limits_0^y {\mu (x)\lambda (x)f(a(x))} dx,} y \leqslant \infty ,$$...
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| Datum: | 2006 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2006
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3528 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Under certain conditions on continuous functions $μ, λ, a$, and $f$, we prove the inequality
$$\int\limits_0^y {\mu (x)\lambda (x)f\left( {\frac{{\int_0^x {\lambda (t)a(t)dt} }}{{\int_0^x {\lambda (t)dt} }}} \right)dx \leqslant K\int\limits_0^y {\mu (x)\lambda (x)f(a(x))} dx,} y \leqslant \infty ,$$
and describe its application to the investigation of the problem of finding conditions under which Laplace integrals belong to a class of convergence. |
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