## Generalized Analytic Functions in Fractional SpacesThis book studies the foundations of the general theory of generalized analytic functions in fractional spaces. The employment of fractional spaces and embedding theorems support applications of the theory of generalized analytic functions. The results obtained are applicable to the theory of singular integral equations, boundary value problems for elliptic differential equations, functions of a complex variable, as well as the theory of plates and shells. The book will be of interest to scientific workers and specialists interested in these questions and likewise to advanced students in mechanical engineering faculties. |

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### Contents

Introduction | 1 |

Properties of several integral operators in fractional spaces | 6 |

Properties of the operators TGf and Ilgf in the spaces B G | 14 |

Continuity of functions of the form Taf | 23 |

Some properties of functions from BataG | 30 |

Properties of the operators Tef and lief | 33 |

On products of functions from Bclasses | 37 |

Complete continuity of certain operators linked to Tof | 41 |

Treatment of the nonlinear integral equation 4 3 | 70 |

Adjoint equation | 72 |

Systems of basic elementary generalized analytic functions and basic kernels of the class VAB1 p 2 a 2p 1 | 73 |

Cauchys generalized formula | 75 |

Expression for the resolvent operator in terms of the basic kernels | 78 |

Representation of generalized analytic functions with the aid of generalized Cauchy type integrals | 81 |

On continuously differentiable homeomorphic solutions | 87 |

Boundary value problems | 95 |

Properties of Cauchytype integrals | 45 |

General theory of generalized analytic functions in fractional spaces | 51 |

An integral equation | 54 |

Differential properties of regular solutions | 57 |

Further extensions of the solution concept A basic lemma and properties of generalized solutions | 59 |

Solvability of integral equations of the form 2 1 | 64 |

Generalized analytic functions in unbounded domains | 107 |

The properties of the operator Tf in Lpp 1 | 117 |

132 | |

Index of Names | 139 |

### Common terms and phrases

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