Electronic Resource
Springer
The journal of Fourier analysis and applications
1 (1994), S. 201-232
ISSN:
1531-5851
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In the spirit of work of Kerman and Sawyer, a condition is given that is necessary and sufficient for the Fourier transform norm inequality $\Big(\int_{{\Bbb R}_d} \vert\hat{f}\vert^q d\mu\Big)^{1/q} \leq C\Big(\int_{{\Bbb R}_d} \vert f\vert^p v\Big)^{1/p}$ provided v is a radial weight for which v−1/p is convexly decreasing and μ is a suitable measure. We also establish alternative conditions for such inequalities by proving corresponding trace type inequalities and maximal function inequalities that underlie the Fourier transform estimates. Our conditions are relatively simple to compute. Among applications we give extensions of a Sobolev restriction theorem.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s00041-001-4010-y
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