We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial $BV$ bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal equicontinuity in $L^1$ of the approximations, uniformly in the viscosity coefficient. Using these estimates, we supply a multidimensional existence theory of stochastic entropy solutions. In addition, we establish an error estimate for the stochastic viscosity method, as well as an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux and random source functions. Various further generalizations of the results are discussed

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<abstract><p>In this paper, we characterize when the product of two H-Toeplitz operators to be another H-Toeplitz with one general and another quasihomogeneous symbols. Also, we describe the product of H-Toeplitz operator and Toeplitz operator to be another H-Toeplitz with certain harmonic symbols.</p></abstract>

On the harmonic Dirichlet space of the unit disk, the commutativity of Toeplitz and Hankel operators is studied. We obtain characterizations of commuting Toeplitz and Hankel operators and essentially commuting (semicommuting) Toeplitz and Hankel operators with general symbols.