Riesz means of Fourier series and integrals: Strong summability at the critical index
Riesz means of Fourier series and integrals: Strong summability at the critical index
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DOI：
10.1090/tran/7818
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发表时间：
2018-07
影响因子：
1.3
通讯作者：
Jongchon Kim;A. Seeger
中科院分区：
文献类型：
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作者：
Jongchon Kim;A. Seeger
我们考虑多重Fourier级数的球面Riesz平均和一些推广。虽然Riesz平均在临界指数（d − 1）/2（d-1）/2处的几乎处处收敛对于哈代空间h1（Td）h^1（\mathbb T ^d）中的函数可能失败，但我们证明了几乎处处强可和性的尖锐的正结果。对于Lp（Td）L ^p（\mathbb T ^d），1> p> 2 1> p> 2中的函数，我们考虑临界指数为d（1/p − 1/2）− 1/2 d（1/p-1/2）-1/2的Riesz平均，并证明了一个关于强可和性的几乎尖锐定理.所得结果是从傅里叶积分的相应结果移植而来的。我们在哈代空间Hp（Rd）H ^p（\mathbb {R}^d）（0> p> 1 0> p> 1）上包含了与广义Riesz平均相关的极大算子的端点界.
We consider spherical Riesz means of multiple Fourier series and some generalizations. While almost everywhere convergence of Riesz means at the critical index ( d − 1 ) / 2 (d-1)/2 may fail for functions in the Hardy space h 1 ( T d ) h^1(\mathbb T^d) , we prove sharp positive results for strong summability almost everywhere. For functions in L p ( T d ) L^p(\mathbb T^d) , 1 > p > 2 1>p>2 , we consider Riesz means at the critical index d ( 1 / p − 1 / 2 ) − 1 / 2 d(1/p-1/2)-1/2 and prove an almost sharp theorem on strong summability. The results follow via transference from corresponding results for Fourier integrals. We include an endpoint bound on maximal operators associated with generalized Riesz means on Hardy spaces H p ( R d ) H^p(\mathbb {R}^d) for 0 > p > 1 0>p>1 .