Hiroki Saito

activity

20142026

most citedChoquet integrals, Hausdorff content and fractional operators

5 citations · 7 across the 8 of their papers we have counts for

collaborators

9 papers

math.FA2026

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…

math.FA2026

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.

math.FA2026

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…

math.FA2023

Choquet integrals, Hausdorff content and sparse operators

Naoya Hatano, Ryota Kawasumi, Hiroki Saito +1

Let $H^{d}$ , $0 < d < n$ , be the dyadic Hausdorff content of the $n$ -dimensional Euclidean space $R^{n}$ . It is shown that $H^{d}$ counts a~Cantor set of the unit cube $[0, 1)^{n}$ a…

math.FA2023★ 5 cited

Choquet integrals, Hausdorff content and fractional operators

Naoya Hatano, Ryota Kawasumi, Hiroki Saito +1

It is shown that the fractional integral operator $I_{α}$ , $0 < α < n$ , and the fractional maximal operator $M_{α}$ , $0 \leq α < n$ , are bounded on weak Choquet spaces with respect to Hausdorff…

math.FA2017

Fractional maximal operators with weighted Hausdorff content

Hiroki Saito, Hitoshi Tanaka, Toshikazu Watanabe

Let $n \geq 2$ be the spatial dimension. The purpose of this note is to obtain some weighted estimates for the fractional maximal operator $M α$ of order $α$ , $0 \leq α < n$ , o…

math.CA2017

The Fefferman-Stein type inequalities for the multilinear strong maximal functions

Juan Zhang, Hiroki Saito, Qingying Xue

Let $ω = (ω_{1}, ..., ω_{m})$ be a multiple weight and ${Ψ_{j}}_{j = 1}^{m}$ be a sequence of Young functions. Let $M_{R}^{Ψ}$ be the multilinear strong ma…

math.CA2016★ 2 cited

The Fefferman-Stein type inequalities for strong and directional maximal operators in the plane

Hiroki Saito, Hitoshi Tanaka

The Fefferman-Stein type inequalities for strong maximal operator and directional maximal operator are verified with composition of the Hardy-Littlewood maximal operator in the pla…

math.CA2014

The Kakeya maximal operator on the variable Lebesgue spaces

Hiroki Saito, Hitoshi Tanaka

We shall verify the Kakeya (Nikodym) maximal operator $K_{N}$ , $N ≫ 1$ , is bounded on the variable Lebesgue space $L^{p (\cdot)} (R^{2})$ when the exponent function $p(\cdot)…