On Fatou type convergence of higher derivatives of certain nonlinear singular integral operators

Harun Karsli; H. Erhan Altin

doi:10.33993/jnaat421-981

Authors

Harun Karsli Abant Izzet Baysal University, Turkey
H. Erhan Altin Abant Izzet Baysal University, Turkey

DOI:

https://doi.org/10.33993/jnaat421-981

Keywords:

nonlinear singular integral operator, pointwise convergence, Fatou type convergence

Abstract views: 313

Abstract

The present paper concerns with the Fatou type convergence properties of the

r - t h

and

(r + 1) - t h

derivatives of the nonlinear singular integral operators defined as

(I_{λ} f) (x) = \int_{a}^{b} K_{λ} (t - x, f (t)) d t, x \in (a, b),

acting on functions defined on an arbitrary interval

(a, b),

where the kernel

K_{λ}

satisfies some suitable assumptions. The present study is a continuation and extension of the results established in the paper [7].

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References

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