The grand Hardy classes \(H_{p)}^{+}\) and \({}_{m}H_{p)}^{-}\), \(p>1\), of functions analytic inside and outside the unit disk, which are generated by the norms of the grand Lebesgue spaces, are defined. Riemann problems of the theory of analytic functions with piecewise continuous coefficient are considered in these spaces. For these problems in grand Hardy classes, a sufficient solvability condition on the coefficient of the problem is found and a general solution is constructed. It should be noted that grand Lebesgue spaces are nonseparable and, therefore, certain classical facts (for example, part of the Riesz theorem) do not hold in these spaces, as well as in the Hardy spaces generated by them. Therefore, one must find a suitable subspace associated with differential equations and study the problems in these subspaces.

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关于Hardy类中Riemann问题的可解性

内部分析函数的宏类Hardy类\（H_ {p）} ^ {+} \）和\（{} _ {m} H_ {p）} ^ {-} \）\（p> 1 \）并定义了由大Lebesgue空间的范数生成的单位磁盘外部。在这些空间中考虑了具有分段连续系数的解析函数理论的黎曼问题。对于大型Hardy类中的这些问题，找到了关于该问题系数的充分可解性条件，并构造了一个通用解。应当指出，大Lebesgue空间是不可分离的，因此，某些经典事实（例如，Riesz定理的一部分）在这些空间以及它们所生成的Hardy空间中均不成立。因此，必须找到与微分方程相关的合适子空间，并研究这些子空间中的问题。