About Certain Singular Kernels K(x,y) = K1(x-y)K2(x+y).
T. Godoy, M. Urciuolo, L. Saal (1994)
Mathematica Scandinavica
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T. Godoy, M. Urciuolo, L. Saal (1994)
Mathematica Scandinavica
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Dashan Fan, Shuichi Sato (2004)
Studia Mathematica
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We prove some weighted weak type (1,1) inequalities for certain singular integrals and Littlewood-Paley functions.
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.
Carlos Pérez (1997)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
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Egil Heistad (1967)
Mathematica Scandinavica
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Fr. Fabricius-Bjerre (1977)
Mathematica Scandinavica
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Hussain Al-Qassem, Leslie Cheng, Yibiao Pan (2014)
Studia Mathematica
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For any n ∈ ℕ, we obtain a bound for oscillatory singular integral operators with polynomial phases on the Hardy space H¹(ℝⁿ). Our estimate, expressed in terms of the coefficients of the phase polynomial, establishes the H¹ boundedness of such operators in all dimensions when the degree of the phase polynomial is greater than one. It also subsumes a uniform boundedness result of Hu and Pan (1992) for phase polynomials which do not contain any linear terms. Furthermore, the bound is shown...
Tatyana Shaposhnikova (1995)
Mathematica Scandinavica
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Henrik Stetkaer-Hansen (1966)
Mathematica Scandinavica
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Yibiao Pan (1991)
Revista Matemática Iberoamericana
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Kislyakov, S.V., Parilov, D.V. (2005)
Zapiski Nauchnykh Seminarov POMI
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Svante Janson (1977)
Mathematica Scandinavica
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Lars Hörmander (1979)
Mathematica Scandinavica
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Hardy G.H. and J.E. Littlewood (1922)
Mathematische Zeitschrift
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