Laplace-Bessel diferensiyel operatörüne karşılık gelen genelleştirilmiş maksimal fonksiyon ve genelleştirilmiş Riesz potansiyeli

Bu tez, bes bolumden olusmaktadir. Birinci bolum giris kismina ayrildi ve tez hakkindagenel bilgiler verildi. Ikinci bolum, ileri bolumlerde gerekli olan tanim ve teoremleriicermektedir. Ucuncu bolumde Laplace-Bessel diferensiyel operatoru tarafindan uretilenmaksimal fonksiyon ve Riesz potansiyeli tanitilmis ayrica varlik ve sinirlilik ozellikleriincelenmistir. Dorduncu bolumde Genellestirilmis oteleme operatoru yardimiylatanimlanan B-Maksimal fonksiyon ve B-Riesz potansiyeli tanitilmis ve bunlar icinsinirlilik kosullari belirlenmistir. Son bolumde ise, Laplace-Bessel diferensiyeloperatorune karsilik gelen genellestirilmis maksimal fonksiyon ve genellestirilmis Rieszpotensiyeline yer verilmistir.AbstractThis thesis consists of five chapters. The first chapter is devoted to introduction andgeneral informations about thesis. The second chapter contains definitions and theoremsnecessary for next chapters. In the third chapter maximal function and Riesz Potentialwhich are produced by Laplace-Bessel differential operator are introduced and also theproperties of existence and boundness are investigated. In the fourth chapter B-Maximalfuntion and B-Riesz Potential which are defined by generalized translation operator areintroduced,and their boundness conditions are determined. In the last chaptergeneralized maximal function and generalized Riesz potential associated with theLaplace-Bessel differential operator are mentioned.