Strong Cesàro summability of double Fourier integrals

Authors: Brown, G.1; Feng, D.2; Móricz, F.3

Source: Acta Mathematica Hungarica, Volume 115, Numbers 1-2, April 2007 , pp. 1-12(12)

Publisher: Springer

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Abstract:

We prove the following theorem. Assume f ∈ L ∞(R 2) with bounded support. If f is continuous at some point (x 1,x 2) ∈ R 2, then the double Fourier integral of f is strongly q-Cesàro summable at (x 1,x 2) to the function value f(x 1,x 2) for every 0 < q < ∞. Furthermore, if f is continuous on some open subset <EquationSource Format="TEX"><![CDATA[ $$mathcal{G}$$ ]]></EquationSource> of R 2, then the strong q-Cesàro summability of the double Fourier integral of f is locally uniform on <EquationSource Format="TEX"><![CDATA[ $$mathcal{G}$$ ]]></EquationSource> .

Keywords: double Fourier transform and integral; inversion formula; partial (or Dirichlet) integral; summability (C, 1); strong q-Cesàro summability; 42B10

Document Type: Research article

DOI: 10.1007/s10474-007-4185-z

Affiliations: 1: Email: Vice-Chacellor@vcc.usyd.edu.au 2: Email: dfeng@math.ualberta.ca 3: Email: moricz@math.u-szeged.hu

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