Author

Veli Shahmurov

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Preprint Sep 2026

Derivative Embeddings in Vector-Valued Morrey Spaces

We develop an intermediate-derivative theory for Banach-valued evolution classes with Morrey control in time. Let $E_0\hookrightarrow E$ be Banach spaces, $m\ge2$, $1<p<\infty$, and $0\le\lambda<1$. If $u\in\mathcal M^{p,\lambda}(E_0)$ and $u^{(m)}\in\mathcal M^{p,\lambda}(E)$, then every intermediate derivative satisf...

R. Shahmurov, Veli Shahmurov · 0 citations

Preprint Sep 2026

A Morrey-to-Lebesgue Equivalence for Convolution Calder\'on--Zygmund Operators

We prove that, for vector-valued convolution Calder\'on--Zygmund operators, boundedness on a single nontrivial Morrey space is equivalent to the corresponding global $L^p$ boundedness. Thus one Morrey scale already contains the full finite-$p$ boundedness information. The implication from Morrey to $L^p$ is obtained by...

R. Shahmurov, Veli Shahmurov · 0 citations

Preprint Sep 2026

Exact Traces for Vector-Valued Morrey Spaces

Trace spaces determine exactly which initial values are compatible with an evolution class. We identify the exact trace generated by vector-valued Morrey control in time and show that it differs essentially from the classical $L^p$ theory. For a Banach couple $X_1\hookrightarrow X_0$, the trace of the natural Morrey ev...

R. Shahmurov, Veli Shahmurov · 1 citation · ⚡1