• 제목/요약/키워드: multiple singular integrals

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NORM ESTIMATES ON HARDY SPACES AND MULTIPLE SINGULAR INTEGRALS

  • Cho, Yong-Kum
    • 대한수학회지
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    • 제35권2호
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    • pp.295-314
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    • 1998
  • In this article we examine certain distinctive features regarding Hardy spaces of both classical and product notions on $R^{N}$ with our focus on their interrelations through embeddings and restrictions. Applications of our results to multiple singular integrals are included.d.

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MULTIPLE WEIGHTED ESTIMATES FOR MULTILINEAR COMMUTATORS OF MULTILINEAR SINGULAR INTEGRALS WITH GENERALIZED KERNELS

  • Liwen Gao;Yan Lin;Shuhui Yang
    • 대한수학회지
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    • 제61권2호
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    • pp.207-226
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    • 2024
  • In this paper, the weighted Lp boundedness of multilinear commutators and multilinear iterated commutators generated by the multilinear singular integral operators with generalized kernels and BMO functions is established, where the weight is multiple weight. Our results are generalizations of the corresponding results for multilinear singular integral operators with standard kernels and Dini kernels under certain conditions.

Mode III SIFs for interface cracks in an FGM coating-substrate system

  • Monfared, Mojtaba Mahmoudi
    • Structural Engineering and Mechanics
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    • 제64권1호
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    • pp.71-79
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    • 2017
  • In this study, interaction of several interface cracks located between a functionally graded material (FGM) layer and an elastic layer under anti-plane deformation based on the distributed dislocation technique (DDT) is analyzed. The variation of the shear modulus of the functionally graded coating is modeled by an exponential and linear function along the thickness of the layer. The complex Fourier transform is applied to governing equation to derive a system of singular integral equations with Cauchy type kernel. These equations are solved by a numerical method to obtain the stress intensity factors (SIFs) at the crack tips. The effects of non-homogeneity parameters for exponentially and linearly form of shear modulus, the thickness of the layers and the length of crack on the SIFs for several interface cracks are investigated. The results reveal that the magnitude of SIFs decrease with increasing of FG parameter and thickness of FGM layer. The values of SIFs for FGM layer with exponential form is less than the linear form.