5 citations · 7 across the 8 of their papers we have counts for
6 papers · 1 filter
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…
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…
Fractional maximal operators with weighted Hausdorff content
Hiroki Saito, Hitoshi Tanaka, Toshikazu Watanabe
Let be the spatial dimension. The purpose of this note is to obtain some weighted estimates for the fractional maximal operator of order , , o…