Some new Hardy-type inequalities in q-analysis

Baiarystanov, Askar; Persson, Lars‐Erik; Shaimardan, Serikbol; Temirkhanova, Ainur

doi:10.7153/jmi-10-62

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2018

2023

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 7 publications

(1 citation statement)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One interesting topic, q-analogues of the many inequalities derived from classical analysis, has been established. Its use can be seen in works such as [3,8,13,15,17]. These integral inequalities can be used for the study of qualitative and quantitative properties of integrals, see [1,14,19].…”

Section: Introductionmentioning

confidence: 99%

Sharp Constants for Multivariate Hausdorff -Inequalities

Fan

Zhao²

2018

J. Aust. Math. Soc.

View full text Add to dashboard Cite

In this paper, we focus on the multivariate Hausdorff operator of the form $$\begin{eqnarray}\mathbf{H}_{\unicode[STIX]{x1D6F7}}(f)(x)=\int _{(0,+\infty )^{n}}{\displaystyle \frac{\unicode[STIX]{x1D6F7}\big(\frac{x_{1}}{t_{1}},\frac{x_{2}}{t_{2}},\ldots ,\frac{x_{n}}{t_{n}}\big)}{t_{1}t_{2}\cdots t_{n}}}f(t_{1},t_{2},\ldots ,t_{n})\,\mathbf{dt},\end{eqnarray}$$ where $\mathbf{dt}=dt_{1}\,dt_{2}\cdots \,dt_{n}$ or $\mathbf{dt}=d_{q}t_{1}\,d_{q}t_{2}\cdots d_{q}t_{n}$ is the discrete measure in $q$-analysis. The sharp bounds for the multivariate Hausdorff operator on spaces $L^{p}$ with power weights are calculated, where $p\in \mathbb{R}\backslash \{0\}$.

show abstract