• Corpus ID: 238259831

Jackson-Stechkin type inequalities for differentiable functions in weighted Orlicz spaces

@inproceedings{Akgun2021JacksonStechkinTI,
  title={Jackson-Stechkin type inequalities for differentiable functions in weighted Orlicz spaces},
  author={Ramazan Akgun},
  year={2021}
}
In the present work some Jackson Stechkin type direct theorems of trigonometric approximation are proved in Orlicz spaces with weights satisfying some Muckenhoupt's $A_{p}$ condition. To obtain refined version of the Jackson type inequality we prove an extrapolation theorem, Marcinkiewicz multiplier theorem and Littlewood Paley type results. As a consequence refined inverse Marchaud type inequalities are obtained. By means of a realization result we find an equivalence between the fractional… 

References

SHOWING 1-10 OF 41 REFERENCES
Jackson-Type Inequality for Doubling Weights on the Sphere
AbstractIn the one-dimensional case, Jackson's inequality and its converse for weighted algebraic polynomial approximation, as well as many important, weighted polynomial inequalities, such as
Weighted norm inequalities in Lebesgue spaces with Muckenhoupt weights and some applications to operators
Abstract In the present work we give a simple method to obtain weighted norm inequalities in Lebesgue spaces Lp,γ with Muckenhoupt weights γ. This method is different from celebrated Extrapolation or
Littlewood-Paley and multiplier theorems on weighted ^{} spaces
The Littlewood-Paley operator y(f), for functions f defined on RX, is shown to be a bounded operator on certain weighted LP spaces. The weights satisfy an AP condition over the class of all
Approximating Polynomials for Functions of Weighted Smirnov-Orlicz Spaces
Let 𝐺0 and 𝐺∞ be, respectively, bounded and unbounded components of a plane curve Γ satisfying Dini's smoothness condition. In addition to partial sum of Faber series of 𝑓 belonging to weighted
Some inequalities of trigonometric approximation in weighted Orlicz spaces
Abstract In the present work, we proved a refined direct theorem and an exact inverse theorem of trigonometric approximation in Orlicz spaces with weights satisfying some Muckenhoupt’s Ap condition.
Realization and characterization of modulus of smoothness in weighted Lebesgue spaces
We obtain a characterization of modulus of smoothnes of fractional order in the Lebesgue spaces Lω, 1 < p <∞, with weights ω satisfying the Muckenhoupt’s Ap condition. Also, a realization result and
Approximation by trigonometric polynomials in weighted Orlicz spaces
We investigate the approximation properties of the partial sums of the Fourier series and prove some direct and inverse theorems for approximation by polynomials in weighted Orlicz spaces. In
Criteria of weighted inequalities in Orlicz classes for maximal functions defined on homogeneous type spaces
The necessary and sufficient conditions are derived in order that a strong type weighted inequality be fulfilled in Orlicz classes for scalar and vector-valued maximal functions defined on
Ul'yanov Type Inequalities For Moduli Of Smoothness
Let T denote the interval [ �;�]. In this work we investigate the inequality of Ul’yanov type for moduli of smoothness of an integer order in the Lp (T); p � 1 spaces. In particular, we study (p;q)
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