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The boundedness of a bilinear oscillatory integral
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Guoliang Li
Abstract
In this paper, the bilinear oscillatory integral Tβ(f , g)(x) = 1 ∫ −1 f (x − t)g(x + t)ei|t|−β dt |t| , β > 0 is proved to be Lp(ℝ) × Lq(ℝ) → Lr(ℝ) bounded for all 1p + 1q = 1r , 12 < r < ∞, and 1 < p, q < ∞.
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Abstract
In this paper, the bilinear oscillatory integral Tβ(f , g)(x) = 1 ∫ −1 f (x − t)g(x + t)ei|t|−β dt |t| , β > 0 is proved to be Lp(ℝ) × Lq(ℝ) → Lr(ℝ) bounded for all 1p + 1q = 1r , 12 < r < ∞, and 1 < p, q < ∞.
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Kapitel in diesem Buch
- Frontmatter I
- Foreword V
- Contents VII
- Hardy spaces associated to the Kohn Laplacian on a family of model domains in Cn+1 1
- Affine mixed Rayleigh quotients 29
- Riesz potentials and Hardy–Morrey spaces 49
- A conjecture regarding compact Lie groups and its consequences 79
- The singular Fredholm integral operators and related integral equations of Chandrasekhar type 89
- Extended multichannel weighted Schatten p-norm minimization for color image denoising 105
- The boundedness of a bilinear oscillatory integral 123
- On sharp Sobolev-type inequalities for multidimensional Cauchy measures 135
- Banach lattice-valued q-variation and convexity 153
- Weighted boundedness of Marcinkiewicz integral operators and related singular integral operators 167
- A spectral comparison note 195
- On existence and nonexistence of nonnegative solutions to heat equation on Riemannian manifolds 207
- The Neumann problem for the Laplacian in half-spaces 219
- An inequality on the mass of image of rectifiable chain under Lipschitz map 253
- Boundedness of general alternative Gaussian singular integrals on Gaussian variable Lebesgue spaces 261
- Remarks on weak–strong uniqueness for two-fluid model 281
- Coercive inequalities on Carnot groups and applications 291
- On exponential Yang–Mills fields and p-Yang–Mills fields 317
- Index 359
Kapitel in diesem Buch
- Frontmatter I
- Foreword V
- Contents VII
- Hardy spaces associated to the Kohn Laplacian on a family of model domains in Cn+1 1
- Affine mixed Rayleigh quotients 29
- Riesz potentials and Hardy–Morrey spaces 49
- A conjecture regarding compact Lie groups and its consequences 79
- The singular Fredholm integral operators and related integral equations of Chandrasekhar type 89
- Extended multichannel weighted Schatten p-norm minimization for color image denoising 105
- The boundedness of a bilinear oscillatory integral 123
- On sharp Sobolev-type inequalities for multidimensional Cauchy measures 135
- Banach lattice-valued q-variation and convexity 153
- Weighted boundedness of Marcinkiewicz integral operators and related singular integral operators 167
- A spectral comparison note 195
- On existence and nonexistence of nonnegative solutions to heat equation on Riemannian manifolds 207
- The Neumann problem for the Laplacian in half-spaces 219
- An inequality on the mass of image of rectifiable chain under Lipschitz map 253
- Boundedness of general alternative Gaussian singular integrals on Gaussian variable Lebesgue spaces 261
- Remarks on weak–strong uniqueness for two-fluid model 281
- Coercive inequalities on Carnot groups and applications 291
- On exponential Yang–Mills fields and p-Yang–Mills fields 317
- Index 359
