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Taking into account Remark 3.3,.

Moreover, taking into account Remark 2.6 and as for by hypothesis, we get (3.4).

Taking into account Remark 3.4 and the fact that, we get.

If we take into account Remark 4.5 we get the following weak version of Adams result for Morrey spaces.

The same arguments as above show that Theorem 3.1 applies to problem (4.5), taking again into account Remark 3.2.

If we take into account Remark 3.6 we get the following weak version of the Spanne result for Morrey spaces.

Taking into account Remark 3.8, we see that it is the exact complex analogue of Theorem 3.3.

Therefore, applying Theorem 1 and taking into account Remark 1, we can obtain (operatorname{POP}[mathbf{z},mathbf{q} G_{k} z, w)]ge0) for all (k=1,2,3,4).

On combining the representations in (a) and (b), and taking into account Remark 1, we get an alternative direct proof of Theorem 9 if Y has density φ g,K.

Thus, (taking into account Remark 4) in order to determine r t when t+2∈V t, it is enough to find the first period i with i>t+2 and i∉V t and set r t =i−1.