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Journal of Inequalities and Applications

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Open Access 01.12.2006 | Research Article

On weighted inequalities for parametric Marcinkiewicz integrals

verfasst von: H. M. Al-Qassem

Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2006

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Abstract

We establish a weighted

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F91541/MediaObjects/13660_2005_Article_1656_IEq1_HTML.gif

boundedness of a parametric Marcinkiewicz integral operator

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F91541/MediaObjects/13660_2005_Article_1656_IEq2_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F91541/MediaObjects/13660_2005_Article_1656_IEq3_HTML.gif

is allowed to be in the block space

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F91541/MediaObjects/13660_2005_Article_1656_IEq4_HTML.gif

for some

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F91541/MediaObjects/13660_2005_Article_1656_IEq5_HTML.gif

and

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satisfies a mild integrability condition. We apply this conclusion to obtain the weighted

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F91541/MediaObjects/13660_2005_Article_1656_IEq7_HTML.gif

boundedness for a class of the parametric Marcinkiewicz integral operators

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F91541/MediaObjects/13660_2005_Article_1656_IEq8_HTML.gif

and

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related to the Littlewood-Paley

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F91541/MediaObjects/13660_2005_Article_1656_IEq10_HTML.gif

-function and the area integral

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F91541/MediaObjects/13660_2005_Article_1656_IEq11_HTML.gif

, respectively. It is known that the condition

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F91541/MediaObjects/13660_2005_Article_1656_IEq12_HTML.gif

is optimal for the

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F91541/MediaObjects/13660_2005_Article_1656_IEq13_HTML.gif

boundedness of

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Vorheriger Artikel Turan's inequality for appell polynomials

Nächster Artikel Limiting case of the boundedness of fractional integral operators on nonhomogeneous space

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https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F91541/MediaObjects/13660_2005_Article_1656_IEq15_HTML.gif

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Titel: On weighted inequalities for parametric Marcinkiewicz integrals
verfasst von: H. M. Al-Qassem
Publikationsdatum: 01.12.2006
Verlag: Springer International Publishing
Erschienen in: Journal of Inequalities and Applications / Ausgabe 1/2006
Elektronische ISSN: 1029-242X
DOI: https://doi.org/10.1155/JIA/2006/91541

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