The Cesaro Summability Of Fourier Integrals In Rn And Related Problems

The notion of pointwise convergence is not the ideal one in dealing with Fourier series of summability function in fact, Kolmogrov construct a function f∈L(T) with an everywhere divergent Fourier series.Cesaro provides the convergence of the (C,1) sense. It is helpful for us to deal with convergence of the Fourier series.we will extend the problem of Fourier series’s Cesaro in f∈L(T) to the Fourier integral’sCesaro in L(Rn). We give the estimate of convergence problem ofσξf(x) inRn, in this chapter we also give another method of theσξf(x)’s convergence by the Hardy-littlewood maximal function.