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We study properties of weighted Szeg\H{o} and Garabedian kernels on planardomains. Motivated by the unweighted case as explained in Bell's work, thestarting point is a weighted Kerzman-Stein formula that yields boundarysmoothness of the weighted Szeg\H{o} kernel. This provides information on thedependence of the weighted Szeg\H{o} kernel as a function of the weight. Whenthe weights are close to the constant function $1$ (which corresponds to theunweighted case), it is shown that some properties of the unweighted Szeg\H{o}kernel propagate to the weighted Szeg\H{o} kernel as well. Finally, it is shownthat the reduced Bergman kernel and higher order reduced Bergman kernels can bewritten as a rational combination of three unweighted Szeg\H{o} kernels andtheir conjugates, thereby extending Bell's list of kernel functions that aremade up of simpler building blocks that involve the Szeg\H{o} kernel.

Weighted Szeg\H{o} Kernels on Planar Domains