long as the other KT-admissible exponent triplet $\trip$ remains non-endpoint. In such case $\trip$ and $\tript$ are jointly acceptable and satisfy the conditions of the next theorem.

\[thm: infty case\] The estimate $$\label{eq: Strich inhom}
\normQRP{W(t)F}{q}{r}{p} \lesssim \normQRP{F}{\tilde q'}{\tilde r'}{\tilde p'}$$ holds for all $F \in \spaceLqrpd$ in $n= 1$ if and only if $\trip$ and $\tript$ are two jointly KT-acceptable exponent triplets. If $n > 1$ we suppose that $\trip$ and $\tript$ are two jointly KT-acceptable exponent triplets and consider the cases

-   $q,\tilde q < \infty$, $1/q + 1/\tilde q < 1$, and $2\leq r, \tilde r < \infty$: then estimate (\[eq: Strich inhom\]) holds if additionally $$\label{cond: glob inhom}
            \frac {n -1}{p'} < \frac {n}{\tilde{r}}, \quad \frac {n-1}{\tilde{p}'} < \frac {n}{r}.$$

-   $r$, or $\tilde r=\infty$: estimate (\[eq: Strich inhom\]) holds only under the conditions of definition \[dfn: joint accept\], that is if $\triptrip \in \Sigma_1 \cup B$,\
    $\triptrip \in \Sigma_2 \cup C$, respectively.

-   $\tilde q = \infty$: then we have the estimate $$\label{eq: Strich inhom a}
    \normQRP{W(t)F}{q, \tilde p'}{r}{p} \lesssim \normQRP{F}{1}{\tilde r'}{\tilde p'}.$$ Whenever $q \geq \tilde p'$ (\[eq: Strich inhom a\]) implies (\[eq: Strich inhom\]).

-   $q = \infty$: then we have the estimate 