Some convolution inequalities in realized homogeneous Besov and Triebel--Lizorkin spaces

Mohamed Benallia, Madani Moussai

Using the realizations, we study some convolution inequalities in the realized homogeneous Besov spaces $\dot{\tilde B}{^s_{p,q}}(\mathbb R^n)$ and the realized homogeneous Triebel--Lizorkin spaces $\dot{\tilde F}{^s_{p,q}}(\mathbb R^n)$. We also deduce for the homogeneous Sobolev spaces $\dot{W}^m_p(\mathbb R^n)$ in certain sense.