Hausdorff and Dunkl–Hausdorff operators in Lebesgue spaces for monotone functions and monotone weights

Jain, Sandhya; Jain, Pankaj

doi:10.1007/s11117-022-00962-6

Cited by 3 publications

(2 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We observe that in the one-dimensional case Corollary 4.2 and Corollary 4.5 were proved in [7]. Similar results for the one-dimensional Dunkl-Hausdorff operator were obtained in [24]. Two-weight inequalities for the one-dimensional Hausdorff operator were studied in [4] and [31].…”

Section: Examples and Environmentssupporting

confidence: 73%

“…In [23] the boundedness of Dunkl-Hausdorff operator on weighted Lebesgue spaces has been characterized and for a power type weight function the corresponding operator norm has been obtained. Very recently, in [24], the results of [4] were extended for the Dunkl-Hausdorff operator and the boundedness of one-dimensional Hausdorff operator on the cone of non-increasing functions was proved. In the general case for the positive operators weighted integral inequalities were studied in [19].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A characterization of two-weight norm inequalities for multidimensional Hausdorff operators on Lebesgue spaces

Bandaliyev,

Aliyeva

2024

Positivity

View full text Add to dashboard Cite

In this paper we give necessary conditions and sufficient conditions for the boundedness of multidimensional Hausdorff operator on weighted Lebesgue spaces. In particular, we establish necessary and sufficient conditions for the boundedness of special type multidimensional Hausdorff operator on weighted Lebesgue spaces for monotone radial weight functions. Also, we get similar results for important operators of harmonic analysis which are special cases of the multidimensional Hausdorff operator. The results are illustrated by a number of examples.

show abstract

Section: Examples and Environmentssupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

A characterization of two-weight norm inequalities for multidimensional Hausdorff operators on Lebesgue spaces

Bandaliyev,

Aliyeva

2024

Positivity

View full text Add to dashboard Cite

show abstract

BOUNDEDNESS OF DUNKL-HAUSDORFF OPERATOR FOR RADIALLY DECREASING FUNCTIONS AND MONOTONE WEIGHTS ON $$\mathbb {R}^{n}$$

Jain,

Singh,

Madan

et al. 2024

J Math Sci

View full text Add to dashboard Cite

A characterization of two-weight norm inequalities for multidimensionalHausdorff operators on Lebesgue spaces

Bandaliyev

Aliyeva

2023

Preprint

View full text Add to dashboard Cite

In this paper we give necessary conditions and sufficient conditions for the boundedness of multidimensional Hausdorff operator on weighted Lebesgue spaces. In particular, weestablish necessary and sufficient conditions for the boundedness of special type multidimensional Hausdorff operator on weighted Lebesgue spaces for monotone radial weight functions.Also, we get similar results for important operators of harmonic analysis which are specialcases of the multidimensional Hausdorff operator. The results are illustrated by a number ofexamples. Mathematics Subject Classification (2010): 28C99; 46E30; 47G10.

show abstract

Hausdorff and Dunkl–Hausdorff operators in Lebesgue spaces for monotone functions and monotone weights

Cited by 3 publications

References 22 publications

A characterization of two-weight norm inequalities for multidimensional Hausdorff operators on Lebesgue spaces

A characterization of two-weight norm inequalities for multidimensional Hausdorff operators on Lebesgue spaces

BOUNDEDNESS OF DUNKL-HAUSDORFF OPERATOR FOR RADIALLY DECREASING FUNCTIONS AND MONOTONE WEIGHTS ON $$\mathbb {R}^{n}$$

A characterization of two-weight norm inequalities for multidimensionalHausdorff operators on Lebesgue spaces

Contact Info

Product

Resources

About