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1
Content available remote

Divergence of the Bochner-Riesz means in the weighted Hardy spaces

100%
Sato S.
Studia Mathematica
|
1996
|
tom 118
|
nr 3
261-275
EN
We costruct functions in $H_{w}^{1}$ ($w ∈ A_{1}$) whose Fourier integral expansions are almost everywhere non-summable with respect to the Bochner-Riesz means of the critical order.
2
Content available remote

A weighted vector-valued weak type (1,1) inequality and spherical summation

100%
Sato S.
Studia Mathematica
|
1994
|
tom 109
|
nr 2
159-170
EN
We prove a weighted vector-valued weak type (1,1) inequality for the Bochner-Riesz means of the critical order. In fact, we prove a slightly more general result.
3
Content available remote

Estimates for singular integrals and extrapolation

100%
Sato S.
Studia Mathematica
|
2009
|
tom 192
|
nr 3
219-233
EN
We study singular integrals with rough kernels, which belong to a class of singular Radon transforms. We prove certain estimates for the singular integrals that are useful in an extrapolation argument. As an application, we prove $L^{p}$ boundedness of the singular integrals under a certain sharp size condition on their kernels.
4
Content available remote

Weighted weak type (1,1) estimates for oscillatory singular integrals

100%
Sato S.
Studia Mathematica
|
2000
|
tom 141
|
nr 1
1-24
EN
We consider the $A_1$-weights and prove the weighted weak type (1,1) inequalities for certain oscillatory singular integrals.
5
Content available remote

Maximal singular integrals on product homogeneous groups

64%
Ding Y., Sato S.
Studia Mathematica
|
2014
|
tom 222
|
nr 1
41-49
EN
We prove $L^{p}$ boundedness for p ∈ (1,∞) of maximal singular integral operators with rough kernels on product homogeneous groups under a sharp integrability condition of the kernels.
6
Content available remote

Weighted weak type (1,1) estimates for singular integrals and Littlewood-Paley functions

64%
Fan D., Sato S.
Studia Mathematica
|
2004
|
tom 163
|
nr 2
119-136
EN
We prove some weighted weak type (1,1) inequalities for certain singular integrals and Littlewood-Paley functions.
7
Content available remote

On weighted weak type norm inequalities for one-sided oscillatory singular integrals

51%
Fu Z., Lu S., Sato S., Shi S.
Studia Mathematica
|
2011
|
tom 207
|
nr 2
137-151
EN
We consider one-sided weight classes of Muckenhoupt type and study the weighted weak type (1,1) norm inequalities for a class of one-sided oscillatory singular integrals with smooth kernel.
8
Content available remote

Weighted inequalities on product domains

26%
Sato S.
Studia Mathematica
|
1989
|
tom 92
|
nr 1
59-72
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