6 citations · 14 across the 11 of their papers we have counts for
13 papers
High-Probability Guarantees for SGD under -Heavy-Tailed Gradient Noise
Qijun Tong, Masahiro Ikeda, Ryota Kawasumi
Stochastic gradient descent (SGD) is widely used to train machine learning models, but subsampling the training data introduces noise into its updates. The strength and applicabili…
Multilinear embedding theorem for fractional sparse operators
Naoya Hatano, Ryota Kawasumi, Hiroki Saito +1
We show some simple sufficient conditions for which the multilinear embedding theorem holds for fractional sparse operators. By verifying these conditions, we establish the theorem…
The Adams trace theorem for product Morrey spaces
Naoya Hatano, Ryota Kawasumi, Hiroki Saito +1
By using a Hedberg-type inequality, the Adams trace inequality is extended from Lebesgue spaces to product Morrey spaces.
The Kerman-Sawyer trace theorem for product Morrey spaces
Naoya Hatano, Ryota Kawasumi, Hiroki Saito +1
By using parallel corona decomposition, the Kerman-Sawyer trace theorem is extended from Lebesgue spaces to \textit{product Morrey spaces}. By discretizing the multilinear fraction…
Boundedness of composition operators from Lorentz spaces to Orlicz spaces
Naoya Hatano, Masahiro Ikeda, Ryota Kawasumi
The boundedness (continuity) of composition operators from some function space to another one is significant, though there are few results about this problem. Thus, in this study,…
Boundedness of composition operator in Orlicz-Morrey spaces
Masahiro Ikeda, Isao Ishikawa, Ryota Kawasumi
In this paper, we investigate necessary and sufficient conditions on the boundedness of composition operators on the Orlicz-Morrey spaces. The results of boundedness include Lebesg…
Choquet integrals, Hausdorff content and sparse operators
Naoya Hatano, Ryota Kawasumi, Hiroki Saito +1
Let , , be the dyadic Hausdorff content of the -dimensional Euclidean space . It is shown that counts a~Cantor set of the unit cube a…
Choquet integrals, Hausdorff content and fractional operators
Naoya Hatano, Ryota Kawasumi, Hiroki Saito +1
It is shown that the fractional integral operator , , and the fractional maximal operator , , are bounded on weak Choquet spaces with respect to Hausdorff…
Pointwise convergence of Fourier series and deep neural network for the indicator function of d-dimensional ball
Ryota Kawasumi, Tsuyoshi Yoneda
In this paper, we clarify the crucial difference between a deep neural network and the Fourier series. For the multiple Fourier series of periodization of some radial functions on…
Weighted boundedness of the Hardy-Littlewood maximal and Calderón-Zygmund operators on Orlicz-Morrey and weak Orlicz-Morrey spaces
Ryota Kawasumi, Eiichi Nakai
For the Hardy-Littlewood maximal and Calderón-Zygmund operators, the weighted boundedness on the Lebesgue spaces are well known. We extend these to the Orlicz-Morrey spaces. Moreov…
Characterization of the boundedness of generalized fractional integral and maximal operators on Orlicz-Morrey and weak Orlicz-Morrey spaces
Ryota Kawasumi, Eiichi Nakai, Minglei Shi
We give necessary and sufficient conditions for the boundedness of generalized fractional integral and maximal operators on Orlicz-Morrey and weak Orlicz-Morrey spaces. To do this…
Predual of weak Orlicz spaces
Naoya Hatano, Ryota Kawasumi, Takahiro Ono
In this paper, we consider the predual spaces of weak Orlicz spaces. As an application, we provide the Fefferman-Stein vector-valued maximal inequality for the weak Orlicz spaces.…
Pointwise multipliers on weak Orlicz spaces
Ryota Kawasumi, Eiichi Nakai
We characterize the pointwise multipliers from a weak Orlicz space to another weak Orlicz space.