In this paper, we give a generalization of Fefferman-Stein inequality for the fractional one-sided maximal operator: Z +∞ −∞ M α (f)(x) w(x) dx ≤ Ap Z +∞ −∞ |f(x)|M αp(w)(x) dx, where 0 < α < 1 and 1 < p < 1/α. We also obtain a substitute of dual theorem and weighted norm inequalities for the one-sided fractional integral I α .

In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of Rn. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams’ results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels sati...

In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of Rn. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams’ results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels sati...

Integral inequalities have accumulated a comprehensive and prolific field of research within mathematical interpretations. In recent times, strategies fractional calculus become the subject intensive in historical contemporary generations because their applications various branches science. this paper, we concentrate on establishing Hermite–Hadamard Pachpatte-type integral with aid two differen...

In this research, generalizations of midpoint type inequalities are established. h-convexity is used as a tool. These for differentiable functions which involve Riemann-Liouville fractional integrals. Also, some consequences these established obtained.