从ItemsControl派生的WPF自定义控件无法显示绑定数据

public CustomItemsControl()
{
    this.DataContext = this;
}

public class CustomItemsControl : ItemsControl
{
    public static readonly DependencyProperty ItemsProperty =
        DependencyProperty.Register("Items", typeof(IEnumerable), typeof(CustomItemsControl));

    public IEnumerable Items
    {
        get { return (IEnumerable)GetValue(ItemsProperty); }
        set { SetValue(ItemsProperty, value); }
    }
}

<CustomItemsControl Items="{Binding}">
    <CustomItemsControl.ItemTemplate>
        <DataTemplate>
            <!-- 控件的可视化元素 -->
        </DataTemplate>
    </CustomItemsControl.ItemTemplate>
</CustomItemsControl>

<Window x:Class="MainWindow"
        xmlns:local="clr-namespace:YourNamespace"
        xmlns:sys="clr-namespace:System;assembly=mscorlib">
    <Window.Resources>
        <sys:String x:Key="Item1">Item 1</sys:String>
        <sys:String x:Key="Item2">Item 2</sys:String>
    </Window.Resources>
    
    <Grid>
        <local:CustomItemsControl Items="{Binding Source={StaticResource Item1}}">
            <local:CustomItemsControl.ItemTemplate>
                <DataTemplate>
                    <TextBlock Text="{Binding}" />
                </DataTemplate>
            </local:CustomItemsControl.ItemTemplate>
        </local:CustomItemsControl>
    </Grid>
</Window>