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Harmonic Analysis Komaba Seminar
Seminar information archive ～04/26｜Next seminar｜Future seminars 04/27～
| Date, time & place | Saturday 13:00 - 18:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|
2013/04/20
13:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hiroki Saito (Tokyo Metropolitan University) 13:30-15:00
Directional maximal operators and radial weights on the plane
(JAPANESE)
Boundedness of Trace operator for Besov spaces with variable
exponents
(JAPANESE)
Hiroki Saito (Tokyo Metropolitan University) 13:30-15:00
Directional maximal operators and radial weights on the plane
(JAPANESE)
[ Abstract ]
Let $\\Omega$ be a set of unit vectors and $w$ be a radial weight on the plane. We consider the weighted directional maximal operator defined by
$M_{\\Omega,w}f(x):=\\sup_{x\\in R\\in \\cB_{\\Omega}}\\frac{1}{w(R)}\\int_{R}|f(y)|w(y)dy$,
where $\\cB_{\\Omega}$ denotes the all rectangles on the plane whose longest side is parallel to some unit vector in $\\Omega$ and $w(R)$ denotes $\\int_{R}w$.
In this talk we give a sufficient condition of the weight
for an almost-orthogonality principle related to these maximal operators to hold. The condition allows us to get weighted norm inequality
$\\|M_{\\Omega,w}f\\|_{L^2(w)}\\le C \\log N \\|f\\|_{L^2(w)}$,
when $w(x)=|x|^a$, $a>0$, and $\\Omega$ is a set of unit vectors on the plane with cardinality $N\\gg 1$.
Takahiro Noi (Chuo University) 15:30-17:00Let $\\Omega$ be a set of unit vectors and $w$ be a radial weight on the plane. We consider the weighted directional maximal operator defined by
$M_{\\Omega,w}f(x):=\\sup_{x\\in R\\in \\cB_{\\Omega}}\\frac{1}{w(R)}\\int_{R}|f(y)|w(y)dy$,
where $\\cB_{\\Omega}$ denotes the all rectangles on the plane whose longest side is parallel to some unit vector in $\\Omega$ and $w(R)$ denotes $\\int_{R}w$.
In this talk we give a sufficient condition of the weight
for an almost-orthogonality principle related to these maximal operators to hold. The condition allows us to get weighted norm inequality
$\\|M_{\\Omega,w}f\\|_{L^2(w)}\\le C \\log N \\|f\\|_{L^2(w)}$,
when $w(x)=|x|^a$, $a>0$, and $\\Omega$ is a set of unit vectors on the plane with cardinality $N\\gg 1$.
Boundedness of Trace operator for Besov spaces with variable
exponents
(JAPANESE)
