On the Cauchy–Riemann conditions in the class of functions with summable modulus, and some boundary properties of analytic functions

The analyticity of functions that satisfy the Cauchy-Riemann conditions and have summable modulus is established. Thus the Looman–Men'shov and Tolstov theorems are generalized. The theorem of Lindelöf is generalized (from the class of bounded functions to the class $L_1$) for certain kinds of domains. Sufficient criteria for continuity on the boundary for some classes of analytic functions are investigated.
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