منابع مشابه
Endpoint Bounds for a Generalized Radon Transform
We prove that convolution with arclength measure on the curve parametrized by h(t) := (t, t, . . . , t) is a bounded operator from L(R) to L(R) for the full conjectured range of exponents, improving on a result due to M. Christ. We also obtain nearly sharp Lorentz space bounds.
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متن کاملEndpoint Bounds for an Analytic Family of Hilbert Transforms
In R2, we consider an analytic family of operators Hz , z ∈ C, whose convolution kernel is obtained by taking −z − 1 derivatives of arclength measure on the parabola (t, t2) in a homogeneous way, defined in such a way so that H−1 be the standard parabolic Hilbert transform. For a fixed z, we study the set of p for which Hz is bounded on Lp(R2) and for the critical z that captures the degree of ...
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In R2, we consider an analytic family of fractional integrals , whose convolution kernel is obtained by taking some transverse derivatives of arclength measure on the parabola (t, t2) multiplied by |t|γ , and doing so in a homogeneous way. We determine the exact range of p, q for which the analytic family maps Lp to Lq . We also resolve a similar issue on the Heisenberg group.
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2013
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-013-9275-4