10 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…