Logarithmic Bloch Spaces Research Articles

On a new operator from the logarithmic Bloch space to the Bloch-type space on the unit ball

We study the boundedness and compactness of a recently introduced operator denoted by P φ g , which is a kind of the product of composition and integral operators on the unit ball B ⊂ C n , from the logarithmic Bloch space B log and the little logarithmic Bloch space B log, 0 to the Bloch-type space B μ or the little Bloch-type space B μ , 0 .

WEIGHTED COMPOSITION OPERATORS FROM F(p, q, s) INTO LOGARITHMIC BLOCH SPACE

We characterize the boundedness and compactness of the weighted composition operator <TEX>$uC_{\psi}$</TEX> from the general function space F(p, q, s) into the logarithmic Bloch space <TEX>${\beta}_L$</TEX> on the unit disk. Some necessary and sufficient conditions are given for which <TEX>$uC_{\psi}$</TEX> is a bounded or a compact operator from F(p,q,s), <TEX>$F_0$</TEX>(p,q,s) into <TEX>${\beta}_L$</TEX>, <TEX>${\beta}_L^0$</TEX> respectively.