68 citations · 78 across the 14 of their papers we have counts for
14 papers
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…
The -linear embedding theorem for dyadic rectangles
Hitoshi Tanaka, Kozo Yabuta
Let $\sg_i$, , denote reverse doubling weights on , let $\cdr(\R^d)$ denote the set of all dyadic rectangles on (Cartesian products of usual dyadic inter…
Fractional operators on weighted Morrey spaces
Shohei Nakamura, Yoshihiro Sawano, Hitoshi Tanaka
A necessary condition and a sufficient condition for one weight norm inequalities on Morrey spaces to hold are given for the fractional maximal operator and the fractional integral…
The Fefferman-Stein type inequality for strong maximal operator in the heigher dimensions
Hitoshi Tanaka
The Fefferman-Stein type inequality for strong maximal operator is verified with compositions of some maximal operators in the heigher dimensions. An elementary proof of the endpoi…
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…
Equivalent norms for the Morrey spaces with non-doubling measures
Hitoshi Tanaka, Yoshihiro Sawano
In this paper under some growth condition we investigate the connection between RBMO and the Morrey spaces. We do not assume the doubling condition which has been a key property of…
The linear embedding theorem
Hitoshi Tanaka
Let , , denote positive Borel measures on , let denote the usual collection of dyadic cubes in and let $K:\,\mathcal{D…
The trilinear embedding theorem
Hitoshi Tanaka
Let , , denote positive Borel measures on , let denote the usual collection of dyadic cubes in and let $K:\,\mathcal{D}\to[…
Two-weight norm inequalities on Morrey spaces
Hitoshi Tanaka
A description of all the admissible weights similar to the Muckenhoupt class is an open problem for the weighted Morrey spaces. In this paper necessary condition and sufficie…
The Kakeya maximal operator on the variable Lebesgue spaces
Hiroki Saito, Hitoshi Tanaka
We shall verify the Kakeya (Nikodym) maximal operator , , is bounded on the variable Lebesgue space when the exponent function $p(\cdot)…
The Fatou property of block spaces
Yoshihiro Sawano, Hitoshi Tanaka
Around thirty years ago, block spaces, which are the predual of Morrey spaces, had been considered. However, it seems that there is no proof that block spaces satisfy the Fatou pro…
A characterization of two weight trace inequalities for positive dyadic operators in the upper triangle case
Hitoshi Tanaka
Two weight trace inequalities for positive dyadic operators are characterized in terms of discrete Wolff's potentials in the upper triangle case.
A characterization for the boundedness of positive operators in a filtered measure space
Hitosh Tanaka, Yutaka Terasawa
In terms of Sawyer type checking condition, a complete characterization is established for which the positive operator in a filtered measure space is bounded from to $L^q…
Positive operators and maximal operators in a filtered measure space
Hitoshi Tanaka, Yutaka Terasawa
In a filtered measure space, a characterization of weights for which the trace inequality of a positive operator holds is given by the use of discrete Wolff's potential. A refineme…