1 citations · 1 across the 8 of their papers we have counts for
11 papers
Generalization for Poincaré--Sobolev inequalities with local weights
Naoya Hatano
It is well known the local integral inequality which is called Poincaré--Sobolev inequality on each domain cube (or ball). After that many authors investigated the generalization f…
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…
Unconditional uniqueness of Hardy--Hénon parabolic equations on Herz spaces
Naoya Hatano, Masahiro Ikeda
In this paper, we introduce the unconditional uniqueness of solutions in Herz spaces for the Hardy--Hénon parabolic equation, which is a semilinear heat equation with a power-type…
Characterization for Campanato norm via quasi-Banach function spaces not assuming the Fatou property
Naoya Hatano
It is well known that the BMO and Campanato norms can be characterized using the -average. These characterizations were later generalized to averages taken over various types…
Endpoint estimates for commutators with respect to the fractional integral operators on Orlicz-Morrey spaces
Naoya Hatano
It is known that the necessary and sufficient conditions of the boundedness of commutators on Morrey spaces are given by Di Fazio, Ragusa and Shirai. Moreover, according to the res…
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,…
Smoothing estimate for the heat semigroup with a homogeneous weight on Morrey spaces
Naoya Hatano, Masahiro Ikeda
We study the smoothing estimate for the heat semigroup which is related to the nonlinear term of the Hardy-Hénon parabolic equation on Morrey spaces. This result is improvement of…
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…
Atomic decomposition for Morrey-Lorentz spaces
N. Hatano
In this paper, we consider the atomic decomposition for Morrey-Lorentz spaces and applications. Morrey-Lorentz spaces, which have structures of Morrey spaces, Lorentz spaces and th…