Harmonic Analysis Komaba Seminar

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Seminar information archive ～05/20｜Next seminar｜Future seminars 05/21～

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)

[ 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) 15:30-17:00
Boundedness of Trace operator for Besov spaces with variable
exponents
(JAPANESE)

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