2018/11/06 by K. Nagy, Nagy, Károly, Mohamed Salim +1
Mathematics · #42C10 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.1811.06371
openalex publication_date 2018/11/06 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
The properties of the maximal operator of the (C,\α)-means\n(\α=(\α1,\…,\αd)) of the multi-dimensional\nWalsh-Kaczmarz-Fourier series are discussed, where the set of indices is inside\na cone-like set. We prove that the maximal operator is bounded from\nHp^\γ to Lp for p0< p (p0=\max1/(1+\αk): k=1,\…, d)\nand is of weak type (1,1). As a corollary we get the theorem of Simon\n citeS1 on the a.e. convergence of cone-restricted two-dimensional Fej 'er\nmeans of integrable functions. At the endpoint case p=p0, we show that the\nmaximal operator \σ\κ,\α,*L is not bounded from the Hardy\nspace Hp0^\γ to the space Lp0.\n