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The Generalization of Fatou’s Theorem and Its Converse
Dissertation   Open access

The Generalization of Fatou’s Theorem and Its Converse

Tariq Alsmadi
Washington State University
Doctor of Philosophy (PhD), Washington State University
2023
DOI:
https://doi.org/10.7273/000005380
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Abstract

We consider a function K(x) on R n which satisfies certain decay conditions. Let µ be a signed measure on R n . For y > 0 set K[µ](x, y) = Z Rn 1 y n K( x − t y )dµ(t). In this paper we investigate the relationship between the derivative of µ at a point x ∈ R n and the non-tangential limit of K[µ](x, y) (thought of as a function in R n+1 + ).

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