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1

Singular integrals with highly oscillating kernels on product spaces

100%

Prestini E.

Colloquium Mathematicum

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2000

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tom 86

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nr 1

9-13

EN

We prove the $L^{2}(𝕋^{2})$ boundedness of the oscillatory singular integrals $P_{0} f(x,y)=\int_{D_{x}} {{e^{i(M_2(x)y' + M_1(x)x')}}οver{x'y'}} f(x-x',y-y')dx'dy'$ for arbitrary real-valued $L^{∞}$ functions $M_{1}(x), M_{2}(x)$ and for rather general domains $D_{x} ⊆ 𝕋^{2}$ whose dependence upon x satisfies no regularity assumptions.

2

Convergence a.e. of spherical partial Fourier integrals on weighted spaces for radial functions: endpoint estimates

63%

Carro M., Prestini E.

Studia Mathematica

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2009

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tom 192

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nr 2

173-194

EN

We prove some extrapolation results for operators bounded on radial $L^{p}$ functions with p ∈ (p₀,p₁) and deduce some endpoint estimates. We apply our results to prove the almost everywhere convergence of the spherical partial Fourier integrals and to obtain estimates on maximal Bochner-Riesz type operators acting on radial functions in several weighted spaces.

3

Operators of Bochner-Riesz type for the helix

32%

Prestini E.

Studia Mathematica

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1984

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tom 79

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nr 1

7-16

Ograniczanie wyników

2 Studia Mathematica

1 Colloquium Mathematicum

3 Prestini E.

1 Carro M.

1 2009

1 2000

1 1984

Singular integrals with highly oscillating kernels on product spaces

Convergence a.e. of spherical partial Fourier integrals on weighted spaces for radial functions: endpoint estimates

Operators of Bochner-Riesz type for the helix