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Strong Cesáro summability of triple Fourier integrals

Mishra V. N., Khatri K., Mishra L. N.

Fasciculi Mathematici

2014

Nr 53

95--112

The theory of summability is a very extensive field, which has various applications. We prove the following theorem. Assume ƒ ϵ L∞(R3) with bounded support. If ƒ is continuous at some point (x1, x2, X3) ϵ R3, then the triple Fourier integral of ƒ is strongly q-Casáro summable at (x1, x2, X3) to the function value ƒ (x1, x2, X3) for every 0 < q < ∞. Furthermore, if ƒ is continuous on some open subset G of R3, then the strong q-Cesáro summability of the triple Fourier integral of ƒ is locally uniform on G.