A new maximal function is introduced in the dual spaces of test function spaces on spaces of homogeneous type. Using this maximal function, we get new characterization of atomic H^p spaces.
For the plane curves Γ,the maximal operator associated to it is defined by Mf(x)=sup|∫f(x-Γ(t))(r^(-1)t)r^(-1)dt| where is a Schwartz function.For a certain class of curves in R^2,M is shown to bounded on (H(R^2)...For the plane curves Γ,the maximal operator associated to it is defined by Mf(x)=sup|∫f(x-Γ(t))(r^(-1)t)r^(-1)dt| where is a Schwartz function.For a certain class of curves in R^2,M is shown to bounded on (H(R^2),Weak L^1(R^2).This extends the theorem of Stein & Wainger and the theo- rem of Weinberg.展开更多
In this paper,we introduce thickr-sensitivity,multi-r-sensitivity and block thick r-sensitivity for r≥2.We first give a characterization of a minimal system which is block thickly r-sensitive.Then we obtain a suffici...In this paper,we introduce thickr-sensitivity,multi-r-sensitivity and block thick r-sensitivity for r≥2.We first give a characterization of a minimal system which is block thickly r-sensitive.Then we obtain a sufficient condition of a minimal system which is thickly r-sensitive.The maximal pattern entropy of a multi-r-sensitive topological dynamical system is also discussed.展开更多
文摘A new maximal function is introduced in the dual spaces of test function spaces on spaces of homogeneous type. Using this maximal function, we get new characterization of atomic H^p spaces.
文摘For the plane curves Γ,the maximal operator associated to it is defined by Mf(x)=sup|∫f(x-Γ(t))(r^(-1)t)r^(-1)dt| where is a Schwartz function.For a certain class of curves in R^2,M is shown to bounded on (H(R^2),Weak L^1(R^2).This extends the theorem of Stein & Wainger and the theo- rem of Weinberg.
文摘In this paper,we introduce thickr-sensitivity,multi-r-sensitivity and block thick r-sensitivity for r≥2.We first give a characterization of a minimal system which is block thickly r-sensitive.Then we obtain a sufficient condition of a minimal system which is thickly r-sensitive.The maximal pattern entropy of a multi-r-sensitive topological dynamical system is also discussed.
