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Displaying similar documents to “Estimates for oscillatory singular integrals on Hardy spaces”

Oscillatory singular integrals on weighted Hardy spaces

Yue Hu (1992)

Studia Mathematica

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Let T f ( x ) = p . v . ʃ ℝ ¹ e i P ( x - y ) f ( y ) / ( x - y ) d y , where P is a real polynomial on ℝ. It is proved that T is bounded on the weighted H¹(wdx) space with w ∈ A₁.

An oscillatory singular integral operator with polynomial phase

Josfina Alvarez, Jorge Hounie (1999)

Studia Mathematica

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We prove the continuity of an oscillatory singular integral operator T with polynomial phase P(x,y) on an atomic space H P 1 related to the phase P. Moreover, we show that the cancellation condition to be imposed on T holds under more general conditions. To that purpose, we obtain a van der Corput type lemma with integrability at infinity.

L boundedness of a singular integral operator.

Dashan Fan, Yibiao Pan (1997)

Publicacions Matemàtiques

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In this paper we study a singular integral operator T with rough kernel. This operator has singularity along sets of the form {x = Q(|y|)y'}, where Q(t) is a polynomial satisfying Q(0) = 0. We prove that T is a bounded operator in the space L2(Rn), n ≥ 2, and this bound is independent of the coefficients of Q(t). We also obtain certain Hardy type inequalities related to this operator.

Rough oscillatory singular integrals on ℝⁿ

Hussain Mohammad Al-Qassem, Leslie Cheng, Yibiao Pan (2014)

Studia Mathematica

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We establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. The kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log deg(P), which is optimal and was first obtained by Papadimitrakis and Parissis (2010) for kernels without any radial roughness. Among key ingredients of our methods are an L¹ → L² estimate and extrapolation.

New equivalent conditions for Hardy-type inequalities

Alois Kufner, Komil Kuliev, Gulchehra Kulieva, Mohlaroyim Eshimova (2024)

Mathematica Bohemica

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We consider a Hardy-type inequality with Oinarov's kernel in weighted Lebesgue spaces. We give new equivalent conditions for satisfying the inequality, and provide lower and upper estimates for its best constant. The findings are crucial in the study of oscillation and non-oscillation properties of differential equation solutions, as well as spectral properties.

An estimation for a family of oscillatory integrals

Magali Folch-Gabayet, James Wright (2003)

Studia Mathematica

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Let K be a Calderón-Zygmund kernel and P a real polynomial defined on ℝⁿ with P(0) = 0. We prove that convolution with Kexp(i/P) is continuous on L²(ℝⁿ) with bounds depending only on K, n and the degree of P, but not on the coefficients of P.