Weight inequalities for singular integrals defined on spaces of homogeneous and nonhomogeneous type (Q2726696)
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scientific article; zbMATH DE number 1621368
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weight inequalities for singular integrals defined on spaces of homogeneous and nonhomogeneous type |
scientific article; zbMATH DE number 1621368 |
Statements
19 December 2001
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singular integral
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maximal function
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Hardy-type operator
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space of homogeneous type
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space of nonhomogeneous type
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Lorentz space
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Weight inequalities for singular integrals defined on spaces of homogeneous and nonhomogeneous type (English)
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Optimal sufficient conditions are found in weighted Lorentz spaces for weight functions which provide the boundedness of the Calderón-Zygmund singular integral operator defined on spaces of homogeneous and nonhomogeneous type. By a space of nonhomogeneous type the authors mean a measure space with a quasimetric; however, the doubling condition is not assumed and may fail. In the nonhomogeneous case, the results of the authors are also new even in Lebesgue spaces.
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