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

Key:
Free Content - Free Content
New Content - New Content
Subscribed Content - Subscribed Content
Free Trial Content - Free Trial Content

Abstract:

We prove the following theorem. Assume fL (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

The full text electronic article is available for purchase. You will be able to download the full text electronic article after payment.

$47.00 plus tax      Refund Policy

 

OR

Back to top

Key:
Free Content - Free Content
New Content - New Content
Subscribed Content - Subscribed Content
Free Trial Content - Free Trial Content
Share this item with others: These icons link to social bookmarking sites where readers can share and discover new web pages.
Page Help Click here for Page Help
Shopping cart
Tools
Sign in






Need to register?
Sign up here
Text size: A | A | A | A