The Weighted Grand Lebesgue Class of Harmonic Functions and the Dirichlet Problem - Bilalov, B. T.; Ahmedzade, N. R.; Kasumov, Z. A. (PLEIADES PUBLISHING LTD, 2025)
In this paper, we introduce the weighted grand Lebesgue class h(p))(;w) of harmonic function in unit ball omega={z is an element of C:|z| (+)=[0,+infinity]satisfy the A(p) Muckenhoupt condition. It is proved the unique solvability of the Dirichlet problem for La place equation with an arbitrary boundary value from weighted grand Lebesgue space L-p);w(partial derivative omega)on partial derivative omega.
Keywords: weighted grand Lebesgue space; harmonic functions; Muckenhoupt class; Dirichlet problem; PIECEWISE-LINEAR PHASE; MIXED PROBLEM; BOUNDARY-VALUE; LAPLACE EQUATION; SOLVABILITY; SYSTEM; EXPONENTS; BASICITY; SPACES; Mathematics