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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Weighted norm inequalities for singular and fractional integrals


Authors: Benjamin Muckenhoupt and Richard L. Wheeden
Journal: Trans. Amer. Math. Soc. 161 (1971), 249-258
MSC: Primary 47.70
MathSciNet review: 0285938
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Abstract: Inequalities of the form $ {\left\Vert {{{\left\vert x \right\vert}^\alpha }Tf} \right\Vert _q} \leqq C{\left\Vert {{{\left\vert x \right\vert}^\alpha }f} \right\Vert _p}$ are proved for certain well-known integral transforms, T, in $ {E^n}$. The transforms considered include Calderón-Zygmund singular integrals, singular integrals with variable kernel, fractional integrals and fractional integrals with variable kernel.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0285938-7
PII: S 0002-9947(1971)0285938-7
Keywords: Singular integrals, fractional integrals, weighted norm inequalities
Article copyright: © Copyright 1971 American Mathematical Society