Binding to UserControl DependencyProperty

I have created a UserControl with some DependencyProperties (in the example here only one string property). When I instantiate the Usercontrol, I can set the property of the UserControl and it is shown as expected. When I am trying to replace the static text by Binding, nothing is displayed.

My UserControl looks as follows:

<User Control x:Class="TestUserControBinding.MyUserControl"
             xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
             xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006" 
             xmlns:d="http://schemas.microsoft.com/expression/blend/2008" 
             mc:Ignorable="d" 
             d:DesignHeight="30" d:DesignWidth="100">
    <Grid>
    <Label Content="{Binding MyText}"/>
  </Grid>
</UserControl>

The Code Behind is:

namespace TestUserControBinding {

  public partial class MyUserControl : UserControl {
    public MyUserControl() {
      InitializeComponent();
      this.DataContext = this;
    }

    public static readonly DependencyProperty MyTextProperty = 
                   DependencyProperty.Register(
                         "MyText", 
                          typeof(string), 
                          typeof(MyUserControl));

    public string MyText {
      get {
        return (string)GetValue(MyTextProperty);
      }
      set {
        SetValue(MyTextProperty, value);
      }
    }// MyText
    
  }
}

When I try this in my MainWindow, everything is as expected:

<Window x:Class="TestUserControBinding.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns