@ARTICLE{TBA, 

TITLE={[FORTHCOMING] Composition operators from harmonic Bergman and Hardy spaces into weighted harmonic Bloch spaces}, 
  
AUTHOR={Mahmoud Ali Bakhit, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={}, 

NUMBER={Forthcoming papers<br>}, 
	
YEAR={2026}, 

URL={https://www.openscience.fr/Composition-operators-from-harmonic-Bergman-and-Hardy-spaces-into-weighted}, 
	
DOI={TBA}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={We characterize the boundedness and compactness of the composition operator $$$ C_{\psi}$$$, induced by an analytic self-map $$$\psi$$$ of the unit disk, acting from the weighted harmonic Bergman space $$$\mathcal{A}^{p}_{\beta}$$$, $$$1 ≤ p ≤ \infty$$$, into the harmonic Bloch spaces $$$\mathcal{B}^{\mu}_H$$$ and $$$\mathcal{B}^{\mu}_{H,0}$$$, where $$$\mu$$$ is a normal weight. The criteria are formulated both in terms of the action of $$$C_{\psi}$$$ on a family of normalized kernel-type test functions and in terms of explicit conditions on the symbol $$$\psi$$$. Analogous characterizations, with independent proofs, are obtained for $$$C_{\psi}$$$ acting from the harmonic Hardy space $$$\mathcal{H}^{q}$$$ into $$$\mathcal{B}^{\mu}_H$$$ and $$$\mathcal{B}^{\mu}_{H,0}$$$. The approach works directly with harmonic mappings and therefore also covers the endpoint cases $$$p=1$$$ and $$$q=1$$$, in which the analytic and co-analytic parts of a mapping in the space need not belong to the corresponding analytic space.}}