Recently the ℒ
(q,λ) spaces have been investigated by many authors and the theory of these spaces has proved to be particularly important for research in partial differential equations (see for example ,  and ).
The equations of elliptic type in these spaces were first studied by C. B. Morrey , , who applied his well-known imbedding theorems, and afterwards by S. Campanato ,  with the aid of isomorphism theorems and the so-called fundamental inequalities due to him.
On the other hand, G. Stampacchia introduced the ℒ
(q,λ) spaces of strong type , the structures of which are more general and complicated than those of ℒ
(q,λ) Spaces in the usual sense, and greater part of them were characterized by him, L. C. Piccinini, Y. Furusho, the author and others (see , -,  and ).